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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/789

By 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.

RELATED VIDEO FROM OUR COURSE
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=>

The number of ways to choose one president out of \(10\) people is 10C1 = 10.
The number of ways to choose two vice-presidents out of the remaining \(9\) people is 9C2 = \(\frac{(9*8)}{(1*2)} = 36.\)
Thus, the number of ways to choose one president and two vice-presidents out of \(10\) people is \(10 * 36 = 360.\)

Therefore, the answer is E.
Answer: E
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