SAT Subject Test Mathematics Level 2

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?

8.

(A) 21

(B) 34

(C) 168

(D) 336

(E) 495