SOLUTION: We want to form two groups of 7 out of 14 students. In how many different ways can this be done?

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Question 1204953: We want to form two groups of
7 out of 14
students. In how many different ways can this be done?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

You can select 7 persons to one group from 14 persons in  C%5B14%5D%5E7 = %2814%2A13%2A12%2A11%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%29 = 3432 different ways.   ANSWER


As soon as you select 7 persons from 14 for one group,
the second group is formed AUTOMATICALLY from the rest of people.


So, the number of ways to form two groups of 7 from 14 people is the same, 
as the number of ways to form two groups of 7 each from 14 people.


ANSWER.  3432 different ways.

Solved.

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Since the order of persons does not matter,  this problem is on  COMBINATIONS.

On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Learn the subject from there.