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# What is the number of different committees of 4 people that can be sel

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Re: What is the number of different committees of 4 people that can be sel [#permalink]
Bunuel wrote:
What is the number of different committees of 4 people that can be selected from a group of 10 people?

A. 20

B. 40

C. 80

D. 120

E. 210

The number of different committees of 4 people that can be selected from a group of 10 people= 10C4 = 210

IMO E
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
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Ways if selecting a committee of 4 people from a total of 10 people = 10C4
10C4 = 10*9*8*7/(4*3*2)
= 210
Ans. = E
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
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Kudos
Top Contributor
Bunuel wrote:
What is the number of different committees of 4 people that can be selected from a group of 10 people?

A. 20

B. 40

C. 80

D. 120

E. 210

Since the order in which we select the committee members does not matter, we can use combinations to solve this question

We can select 4 people from 10 people in 10C4 ways
10C4 = (10)(9)(8)(7)/(4)(3)(2)(1)
= (10)(9)(7)/(3)(1)
= (10)(3)(7)
= 210

ASIDE: Here's a video on how to reduce your calculations when evaluating combinations like 10C4
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
Bunuel wrote:
What is the number of different committees of 4 people that can be selected from a group of 10 people?

A. 20

B. 40

C. 80

D. 120

E. 210

The number of committees that can be selected is:

10C4 = 10! / (4! x 6!) = (10 x 9 x 8 x 7) / (4 x 3 x 2) = 5 x 3 x 2 x 7 = 210.