PrepLattice is an independent test-preparation service and is not affiliated with or endorsed by GMAC, the organization that administers the GMAT. GMAT and GMAT Focus are trademarks of GMAC, used here only to name the exam this question is designed to prepare you for.
A music director must form a 5-member band from a pool of 5 guitarists, 4 drummers, and 3 keyboardists, all of whom are distinct individuals. The band must include at least one drummer, must include strictly more guitarists than drummers, and may include at most one keyboardist. How many different 5-member bands can the director form?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
Correct answer
D
The keyboardist count is capped at one, so split the count on that value; the strictly-more-guitarists-than-drummers condition and the at-least-one-drummer condition then fix which splits are allowed within each case.
Zero keyboardists: the 5 members come from guitarists and drummers, with more guitarists than drummers and at least one drummer. The only splits that satisfy both conditions are 4 guitarists with 1 drummer, C(5,4) × C(4,1) = 5 × 4 = 20, and 3 guitarists with 2 drummers, C(5,3) × C(4,2) = 10 × 6 = 60. This case totals 80.
Exactly one keyboardist: choose the keyboardist in C(3,1) = 3 ways, then fill the remaining 4 seats from guitarists and drummers under the same two conditions. The only valid split is 3 guitarists with 1 drummer, since a 4-and-0 split has no drummer and a 2-and-2 split is not strictly more guitarists than drummers: C(5,3) × C(4,1) = 10 × 4 = 40, and the 3 choices for the keyboardist give 3 × 40 = 120.
Adding the two cases gives 80 + 120 = 200. So the answer is D.
Pick the theme that suits how you work. You can change it anytime.