MathRevolution
[Math Revolution GMAT math practice question]
A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected?
A. 500
B. 280
C. 300
D. 320
E. 360
Take the task of selecting the president and two vice-presidents and break it into
stages.
Stage 1: Select the president
There are 10 people to choose from. So, we can complete stage 1 in
10 ways
Stage 2: Select two people to be the vice-presidents
Since the order in which we select the two people does not matter, we can use
combinations.
We can select 2 people from the remaining 9 people in 9C2 ways (36 ways)
So, we can complete stage 2 in
36 ways
If anyone is interested, we have a free video on calculating combinations (like 9C2) in your head: https://www.gmatprepnow.com/module/gmat- ... /video/789By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select a president and two vice presidents) in
(10)(36) ways (= 360 ways)
Answer: E
Note: the FCP can be used to solve the
MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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