praetorian123 wrote:

Rules

1. Time yourself

2. Solve this problem on a seperate sheet.

3. Write down the solution and your time.

In how many ways can 4 groups of 2 each be selected from a group of 8 students?

1. 1980

2. 2520

3. 3050

4. 3670

5. 3980

[2] 2520 is the correct answer. good work.

I quote the legend akamai here:

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.

More to Come...keep solving

Praetorian