The Rig Ved 1.113.6 and 10.90.11-12;  Yajur Ved  31.11 and Atharv Ved  19.6.6 explain the  origin of four Varn to formless and ineffable Brahm. HE is described as the entire universe visible to the eyes and all other subtle worlds invisible to the eyes, where six communities of divine people, like angels, Pitri, Gandharv, Karm, Dev etc, live. Heaven is His head, Sun and Moon are His eyes, the entire Universe is His body and the Earth is His feet. Braahmn Varn is born from His mouth which symbolically represents the heaven. This divine Varn was created to spread Brahm Gyaan - Vaidik metaphysics amongst all members of society.

Yajur Ved, 31.11 Mantra says - "Braahman is born from His mouth, Kshatriya is born from His arms, Vaishya are born from His Uru (stomach) and Shoodra are born from His feet."

Bhagavad Geetaa, 10.32 says, that the science of soul or metaphysics is the supreme science. Rig Ved, 6.75.10 mentions that a Braahman is the knower of God and Ved. Since the origin of this Varn is from heaven - the kingdom of God which is the place of bliss and supreme knowledge, the followers of this divine profession are to spread the knowledge of Brahm amongst others and bring heavenly conditions ie the City of God on this Earth.

The human senses and sense organs like eyes, etc can visualize and even see with the help of scientific instruments the entire gross universe which is the manifestation of the subtle divine Nature and is extremely powerful, disciplined and benevolent. Nature and the ever-expanding universe and cosmos are mentioned in the Ved as part of His formless body. Symbolism to the various parts of His Body continues in the Vaidik hymns. Kshatriya Varn is born from the most powerful shoulders of God. This Varn has men and women of great strength who are extremely powerful and benevolent. Their divine duty is to destroy all evil and corruption in society. The individuals belonging to this divine profession are rulers, defense services officers, commander-in-chief, bureaucrats, scientists, technicians etc. (Rig Ved, 5.69.2). Their main duty is to protect the people belonging to other three Varn and ensure a corruption free society. All monarchs, kings, queens and elected Presidents are Kshatriya. However, if a ruler's son is not virtuous or incompetent, he is not entitled to rule the state or country (Rig Ved, 4.19.9). The Ashwinaus (scientists) can be both men and women of absolute self-control with scientific outlook (Rig Ved, 1.3.4). Kshatriya are advised to take Som drink for vigor and energy (Rig Ved, 4.45.3). Som drink is some kind of red colored herbal drink, which is slightly intoxicant and should be taken with milk or yogurt.

It is the mother Earth, which renders selfless service to all animate and inanimate life. Vaidik hymns describe the Earth as the feet of the God. Shoodra Varn is born from the Earth and the members of this Varn based on ability, merit and aptitude render selfless service to other three divine professions. Since all parts of the body are equally important and they help each other for a healthy body, so all these divine Varn should assist, cooperate and sustain each other for achieving an ideal society. Rig Ved, 10.90 describes the followers of Shoodra Varn as good at unskilled work, of good physique, handsome and of high character. In the universe, all planets, stars and others perform their allotted task silently and gracefully and it is difficult to say which parts of the gross universe and subtle Prakriti are more important.

The above social scheme of Chatur Varn Aashram is of divine origin being born of the Body of God. Rig Ved, 10.90.12 has a prayer "O, God give luster to Braahman, Kshatriya, Vaishya and Shoodra and to me." The basis of Vaidik social grouping or Varn is pursuit of divine professions with Dharm and Rit (Rig Ved,  10.90.12; Atharv Ved, 19.6.6; Yajur Ved,  31.13 and 17 and Brihadaaranyak Upanishad 1.4.11-14). The individuals pursuing these four divine professions while following Rit and Dharm can eat and drink together. They can marry amongst themselves. In the society they are co-workers for prosperity and should make riches flow (Atharv Ved, 1-15-2 and 4).

Thus individuals belonging to Chatuar Varn Aashram form an egalitarian society and serve each other. All these four Varn (divine professions) are ordained by God. The fifth non-divine "Avarnas , Vritras Kimidin" are not ordained by God. Thus there are five classes dealing with different professions "four divine and the fifth non- divine one". Marplots, sorcerers, bribe takers and givers, exploiters, evil minded people form :Avarnas" - (Rig Ved, 1.76.3, 1.191.8, 2.14.3) - they are not ordained by God. Being Dambhee Purush (sycophants and hypocrites) they aim at honor, power and wealth and pretend as servants of the people. The terms used in Ved for five classes is Panch Kshatinaam, Panch Maanavi etc.

Ved had also visualized that material prosperity alone may turn a number of individuals into A-Varn, Vritra and other evil minded people, resulting in lack of transparency, corrupt practices and make an ideal state and open society into a perverted state and closed society (Rig Ved, 1.191.8, 1.28.4 and 24, 1.76.3, 2.14.3, 4.9.9).

A few other relevant references are given below:
--Female Gurus (preceptors) are mentioned in Rig Ved 3.33.1-3 and can teach Vaidik metaphysics to students.
--Kashtriya Queens who had studied under the Vaidik Education system up to the age of 24 years should take the role of protecting the subjects or citizens during the war if the king dies or injured. She can take the help of the Commander-in-Chief. (Rig Ved, 6.75.3-15).
--Women can attend Vidhta and Sabhaa (religious and political assemblies (Rig Ved, 10.85.26 and 42-47).
--There are many other Mantra and Rik about women studying Ved. Gaargee, Godharaa, Lopaamudraa and many others were the renowned Vaidik Rishikaa of yore.
--Kwaish Aylush, Vaalmeeki, Vyaas became Braahman though born in other Varn.

From the above it is apparent that Ved do not say anywhere that four divine Varn are not by Birth and women and all Varn can study Ved. Even non divine A-Varn can move towards Varn by studying Ved and following their teachings and guidelines.

For more details kindly see chapter "Vedic Society" in Glimpses of Vaidik Metaphysics on Internet.
Website http://www.sabhlokcity.com/metaphysics

Varn and Aashram
As a project requires people from different disciplines like engineers, labors, contractors etc, in the same way different kind of people are required to run the society and for its progress. That is why classification of people under different groups is inevitable. Ved call them Varn, hence there are the groupings of the people under four heads - (1) An intelligent group - people who are mentally strong, responsible for, acquisition, preservation and propagation of knowledge. This is called Braahman Varn or group. (2) A physically strong people group - people who are physically strong and can fight to protect people from others and control the people. This group consisted of fighting people group is called Kshatriya group. (3) Clever in trade and business - people who are good in trading, commerce and business, cattle rearing etc come under this group and are called Vaishya. (4) people who are neither well educated, nor can fight, nor can do any business, they are just good enough to serve others in menial ways, they are kept in this group and are called Shoodra. Their duty is to serve the three other groups.

As to complete a project all kinds of people are needed, in the same to run the society all kinds of people are needed. No one is higher and no one is lower, everybody does his own job. As a project coordinator or engineer is important, so is a labor. In the same way no one group can claim credit for the sustenance of social order in a society. By the same token no one group is superior to other groups, though for functional hierarchy (like King and Sevak), the outward expression of their respect to the other group(s) is mandatory. It is not for the person per say but for the position one is placed in the society [how this position is decided is another subject of discussion]. This is like Indra or Varun is worshipped for their appropriate benefits. These deities are worshipped more for their position rather than as an individual.

The problem starts when the individual who is respected for his position, begins to think that he himself is superior instead of thinking that he is respected only for his position at which he is placed in the societal order, taking the responsibility and act for the benefit of the one who pays respects, not as an individual. Thus these are the Dharm at a broad level in the society.

This was the classification of the society (Varn), now there is another classification at the individual level - of the life of an individual, according to the way of his living throughout his life. This classification is named Aashram. These Aashram are according the age span of a human being. In Kali Yug a human being's age has been regarded 100 years, that is why his life span has been divide according to this period. This Dharm by age, taking accounting for ones physical conditions and capabilities and mental maturity is consistent with all groups of the society. Whether one is Braahman (Parashuraam) or Kshatriya (Dhritraashtra) or Shoodra (Vidur), all retired to forest after their prime age - Sanyaas.

Origin of Varn on Shukla Yajur ved
Shukla Yajur Ved says about origin of Varn - the Brihadaaranyak Upanishad (1-4-11) of Shukla Yajur Ved gives this account - "In the beginning there was only one Varn, that is, Braahman. It was not able to fulfill the needs of society and so it created Kshatriya, the warrior wing."

Brihadaaranyak Upanishad, 1-4-12 & 13 say that - "Even this was not adequate and so it created the trading wing called Vaishya. When this too was not complete, it created the wing of the working class which was called Shoodra and also Pooshan, which means one who feeds and nourishes the society.&quobr

Reference of Varn and Aashram in Ved
The oldest reference to Varna system appears in Rig Veda in Purush Suktam -
"Yatpurusham vyadhidha katidha vyakalpayan, Mukhum kimashya ........"
Here, the question is being asked that “when the gods employed Purush as the sacrificial offering what was his form like? Who appeared from Purush’s mouth, arm, thighs and feet?
The answer is given in the next verse – "Braahamano asya mukhmaseed baahu rajanyakritah, Uru tadasyah yadvaishya padabhyaam sudroajaayat.
Braahman was originated from mouth, Kshatriya from arms, Vaishya from thighs and Shoodra from feet.

In order to have the whole body function properly it is important that each organ functions in a harmonious and designated manner, therefore each organ in the body is equally important.
This indicates that how human society can be organized in four Varn for harmonious operations. It does not indicate any hierarchical categorization leading into superiority or inferiority of any Varn. It does not mention that mouth (head) is more important than feet. Vaidik seers were interested in harmony of the society. These four Varn represent the type of karma (work and responsibilities) corresponding to each Varn.

Similar references to the Varn system appear in several other Vaidik scriptures conveying the same message. The society is divided in to four Varn and compared with the four parts of the body, i.e., head, arms, thighs and feet. A few additional examples with the same message -

--Vishnu Puraan (1:6, 7-8) the four Varn are described as following;
"Braahmanaah kshatriyaa vaishyaah shoodrashchah dwij Sattam,
Padoruvakshasthalato mukhatascha samudgatah.Yajna nishpattaye sarvametad brahamaa chakaar vai,
Chaaturvarnyam mahaabhaaag yagyasaadhanamuttamam

--Bhaagvat Puraan (11.17.13) - "Vipraksha triya vitshoodra mukhabahurupadajaah, Vairaajat Purushaajjaataa ya aatmaachaarlakshanah

--Vaalmeeki Raamaayan (Aranya Kaand; 14.30) - Mukhto brahmana jaatha urasaha kshtriyaastathaa, Oorubhyaam jagnire vaishyaahaa padabhyaam Shoodra iti shrutih

--Mahabharata (Shaanti Parv: 296. 6) four Varn were originated from Brahmaa Prajaapati in similar way.
Mukhajaa brahmanastata baahujaah kshatriyaaha smritaahaa, Oorujaa dhanin rajan padajaahaa parichaarakaah.
--Mahaabhaarat (Shaanti Parv)  Bheeshm Pitaamaha praises the cosmic being represented by four Varn - “Brahmaa vaktram bhujou kshatram kritsnamooroodaram vishaha, Padou yasyaashritaahaa sudraastasmai varnaaatmane namaha”.

Manu Smriti (1.33) - Lokaanaantu vivriddhyartham mukh baahuroop dataha, Braahmanam kshatriyam vaishyam Shoodram cha niravartayata
Manusmriti (1.89-93) describes the duties of all four Varn as following: Sarvasyaa sya tu sargasya guptyartham sa mahaadyutihi, Mukh baahu pajnaanaam prithak karmaanyakal payat Adhyaapanam adhyanam yajanam yaajanam tatha, daanam pratigraham chaiv brahmanaanaam kalpayatPrajaanam rakshanam daanamijyaadhyaayan amevacha, Vishayeshva prashaktischa kshatriyascha samaadishatahPashun aam rakshanam daanam ijyaa adhyayanmaiv cha, vanikpatham kuseedam cha vaishyascha krishimeva chaEkameva tu sudrasya prabhuh karma samaadishat, Eteshaameva varnanaamshushrusha amansuyaya

Geetaa (4.13) four Varn of society were created by Parabrahm, classifying them according to the predominant Gun found in each and assigning corresponding duties to them - “Chaaturvarnyam maya sristam gun karma vibhagsah, tasya kartaraaramapi mam vidyaa kartaaram vyam”

The purpose of this classification, Varn system, is that the society should function harmoniously and every human being spiritually progresses in his/her life.

Geetaa (18.41-44), Manu Smriti and other scriptures describe different attributes of four Varn and the nature of work suited for them based on their inherent instincts and aptitudes. The basis of the Varn classification is clearly based on the Gun and Karm dynamics.
Geetaa goes on to describing the proclivity and duties of all four Varn, ie, Braahman, Kshatriya, Vaishya, and Shoodra.
The four objectives of life namely Dharm, Arth, Kaam and Moksh are common to all Varn. The Moksh is the highest spiritual attainment and each human being can attain it. The path is different for each Varn to achieve the same goals of spiritual development and fulfillment. Every human being belonging to any Varn can achieve the spiritual fulfillment.