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A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected?

A. 240 B. 280 C. 300 D. 320 E. 360

There are two ways of doing.

Either you select one president and then select 2 Vice presidents from remaining(that is 10-1=9 remaining) --10* or You select 2 vice president and then select 1 president from remaining(that is 10-2= 9 remaining) --10C2*8C1

For first way --

No of ways of selecting one President from 10 = 10C1 = 10 ways No of ways of selecting two Vice- President from remaining (9) = 9C2 Total number of ways = 10*9C2= 360 So E is the answer.

A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected?

A. 240 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

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.

A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected?

A. 240 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

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.

Re: A club has 10 members. One president and two vice-presidents are elect
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30 Nov 2018, 01:18

=>

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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