22. The correct answer is (B). To solve this problem without resorting to listingpossibilities, you need to apply the factorial formula as well as a bit of logic. If you thinkof each of the two empty chairs (C1 and C2) as a distinct object along with each of the3 people (X, Y, and Z), the number of permutations is 5! 55 3 4 33 3 2 31 5 120.However, each permutation is coupled with another in which the two empty chairs arereversed — for example:X, Y, Z, C1, C2X, Y, Z, C2, C1Since the question makes no distinction between the chairs, reduce the number ofpermutations by 50 percent, to 60.

THE CORRECT ANSWER IS (B). TO SOLVE THIS PROBLEM WITHOUT RESORTING...

MASTER GMAT 2010 PART 61 POT

22. The correct answer is (B). To solve this problem without resorting to listing

possibilities, you need to apply the factorial formula as well as a bit of logic. If you think

of each of the two empty chairs (C1 and C2) as a distinct object along with each of the

3 people (X, Y, and Z), the number of permutations is 5!

120.

However, each permutation is coupled with another in which the two empty chairs are

reversed — for example:

X, Y, Z, C1, C2

X, Y, Z, C2, C1

Since the question makes no distinction between the chairs, reduce the number of

permutations by 50 percent, to 60.