GMAT Focus EditionQuantitative ReasoningMedium
A project team has 6 members. If 3 members are to be selected to form a subcommittee, how many different subcommittees can be formed?
- A720
- B18
- C20
- D120
Show answer & explanationAnswer & explanation
Correct answer: C. 20
This is a combination problem because the order in which members are selected for the subcommittee does not matter. The formula for combinations is C(n, k) = n! / (k! * (n-k)!), where n=6 and k=3. C(6, 3) = 6! / (3! * 3!) = (6*5*4) / (3*2*1) = 20.
Why the other options are wrong
- A. This is 6! (6 factorial), which is incorrect as it implies selecting all 6 members in all possible orders.
- B. This might come from a partial calculation or misunderstanding of the formula.
- D. This would be the number of permutations (P(6,3) = 6!/(6-3)! = 120), which is incorrect because order does not matter.
Combinations
A combination is a selection of items from a larger set where the order of selection does not matter.
- Used when order of selection is irrelevant.
- Formula: C(n, k) = n! / (k! * (n-k)!).
- Distinguished from permutations where order matters.
Memory trick: Combinations: just a group, no seating chart. Permutations: specific order matters.