In how many ways can 12 people be divided into 2 equal groups? (Assume that the two groups are an equal size but distinct.)

Answer 1

6 and 6

5 and 5 with 2 left over

4 and 4 with 4 left over

3 and 3 with 6 left over

2 and 2 with 8 left over

1 and 1 with 10 left over

6 ways? to divide 12 into 2 equal groups?

unless the question is asking for something different?

maybe the question is assuming just the 6 and 6 division?

and asking how many ways can each of the 12 be assigned to the two equal groups of 6 each?

then another question is does order matter? if not, the question is asking for a calculation of possible combinations

12C6 for one group: 12!/6!6! = 12x11x10x9x8x7/6x5x4x3x2 = 924. Some relatively inexpensive calculators have a nCr function that does the calculation for you.

then the 2nd group has another 6C6 to pick the remaing 6 but that's just 6!/6!1! = 1

so, 924x1 = 924? Once you've selected the 6 for one group, there's only one way to select the remaining 6 for the 2nd group, assuming order does not matter.