A club has 10 members. One president and two vice-presidents are elect

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.


Press Kudos if it helps!!

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

_________________

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

_________________

=>

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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