In how many ways can 4 groups of 2 each be selected from a group of 8 Students?
Is it 8C2 * 6C2 * 4C2 * 2C2 ?
Selecting multiple groups is EXACTLY the same as selecting one group. Let's say you are selecting 2 people from a group of 8. You are actually selected one group of 2 and one group of 6 (Which is an intuitive way of proving why 8C2 = 8C6). In the denominator of combinations with multiple groups, simply put the factorials of the number of people in each group.
2C8 = choose 2 to be IN and choosing 6 to be OUT or 8!/(2!6!)
To choose 4 groups of 2 from 8, the formula is simply 8!/(2!2!2!2!)
If you think of combinations as "adjusted" permutations, we have 8! ways to arrange 8 people, but each of the 4 pairs is an equivalent combination so we need to divide by 2^4.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993