The answer is (D).
PERMUTATIONS AND COMBINATIONS
To be successful with combinations and permutations questions like Example 8, you have to
remember the relevant formulas.
Example 8
That the question asks for “possible” groupings suggests that you should expect it to hinge on
combinations. Of the 12 members, if 8 are seniors, 4 must be non-seniors. The question requires
that 6 of the 8 seniors, and therefore 2 of the 4 non-seniors, be chosen. First find the number of
possible combinations of seniors on the committee; then do the same for non-seniors. The answer
is the product of the two results. (Note: It’s the product, not the sum—which is the trap in (B).)
PERMUTATIONS AND COMBINATIONS FORMULAS
The number of permutations of n distinct objects is:
n! = n(n – 1)(n – 2)···(3)(2)(1)
The number of permutations of n objects, a of which are indistinguishable, and b of which
are indistinguishable, etc., is:
Of the 12 members of a high school drama club, 8 are seniors. The club plans to establish an 8-
member committee to interview potential club members. If exactly 6 members of the committee
must be seniors, how many committees are possible?