Question

There are 11 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?
A) 161,051
B) 462
C) 55,440
D) 120

Answer 1

11C6 -> (11!)/[(5!)(6!)] -> 462

Answer 2

Where did you get the 6! from?

Answer 3

It is from combination theory:

nCx is (n!) / [(x!)(n - x)!]

6! from (11 - 5)!

Answer 4

The 6! should be more evident than the 5! If order counted, then you would have:

11! / 6! because that's 11 x 10 x 9 x 8 x 7 because of 11 candidates for "1st position", 10 for 2nd, etc. And since we don't take order into account here, we divide by 5! because each group would otherwise be overcounted by that factor.