A club has 24 members: 3 freshmen, 6 sophomore, 10 juniors, 5 seniors.
a) How many ways are there to choose a committee of four people with one person designated as the committee chair?
b) How many ways are there to choose a committee of five people with two juniors who serve as the chair and vice chair and three at-large members who are neither juniors nor seniors?
Any help would be greatly appreciated.
For a) I did C(24, 4) * C(4,1) but not sure if that is correct or not. I assumed out of 24 you choose 4 but then 1 of those 4 is the chair.
For b) I did C(10,2) * C(9,3) but I'm pretty sure that is wrong. I got the 10,2 because you pick 2 juniors out of the 10, and the 9,3 because you pick three out of the freshmen + sophomore
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What is the number of different committees of 4 people that can be sel [#permalink]
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What is the number of different committees of 4 people that can be selected from a group of 10 people?A. 20B. 40C. 80D. 120
E. 210
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
Hello,Out of 10 people, we need to select 4 people and this can be done in 10C4 ways.10C4 can be written as 10!/6!*4! = 210 ways. Option E.Regards,
Vivek
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
We are to determine the number of 4 member committees that can be formed from 10 people. This is simple combination problem since order is not important here.So Number of ways = 10C4 = 210. Answer is E.
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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. 20B. 40C. 80D. 120
E. 210
The number of different committees of 4 people that can be selected from a group of 10 people= 10C4 = 210IMO E _________________
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
Ways if selecting a committee of 4 people from a total of 10 people = 10C4 10C4 = 10*9*8*7/(4*3*2) = 210Ans. = E _________________
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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. 20B. 40C. 80D. 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 ways10C4 = (10)(9)(8)(7)/(4)(3)(2)(1)= (10)(9)(7)/(3)(1)= (10)(3)(7)= 210Answer: EASIDE: 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. 20B. 40C. 80D. 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.Answer: E
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Re: What is the number of different committees of 4 people that can be sel [#permalink]
19 Nov 2022, 08:12