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 project lead will form a 4-person task force chosen from 6 analysts and 3 designers, and the task force must include at least 1 designer. The 4 chosen people will then each be assigned to one of 4 distinct roles: lead, scribe, liaison, and reviewer. In how many ways can the lead both choose the task force and assign its roles?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
Correct answer
D
Step 1, select the group with at least 1 designer: all groups C(9,4) = 126, minus the no-designer (all 6 analysts) groups C(6,4) = 15, leaving 126 − 15 = 111 valid groups. Step 2, assign the 4 distinct roles to the 4 chosen people: 4! = 24 orderings per group. Total = 111 × 24 = 2664.
The two false summits are (A) forgetting the roles are distinct (ordered), which stops at 111, and (E) forgetting the at-least-1-designer constraint, which gives 126 × 24 = 3024. The item earns its difficulty by stacking complement-selection with an ordered role assignment.
Pick the theme that suits how you work. You can change it anytime.