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Comment on Committee of 4 people
In how many ways a committee
Plz explain me this.
Take the task of creating a
Take the task of creating a committee and break it into stages.
STAGE 1: Select the 5 men for the committee
Since the order in which we select the men does not matter, we can use combinations.
We can select 5 men from 8 men in 8C5 ways (56 ways)
So, we can complete stage 1 in 56 ways
STAGE 2: Select the 6 women for the committee
We can select 6 women from 10 women in 10C6 ways (210 ways)
So, we can complete stage 2 in 210 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a committee) in (56)(210) ways.
Answer: 11,760 possible committees
https://gre.myprepclub.com/forum
In this question, I used the following approach:
1st case: M*4*3*2*1
2nd case: 4*M*3*2*1
3rd case: 4*3*2*M*1
(I have fixed Martha's seat in each case)
And, then I added the product of these cases which is 72. Lastly, I subtract it by 120. What is wrong with this approach?
Thanks in advance Brent!
Question link: https:/
Question link: https://gre.myprepclub.com/forum/gre-math-challenge-16-martha-invited-4-...
There are actually 4 cases in which Martha is NOT in the middle:
1st case: M*4*3*2*1 (= 24 arrangements)
2nd case: 4*M*3*2*1 (= 24 arrangements)
3rd case: 4*3*2*M*1 (= 24 arrangements)
4th case: 4*3*2*1*M (= 24 arrangements)
TOTAL arrangements where Martha is NOT in the middle = 24 + 24 + 24 + 24 = 96
So, TOTAL arrangements where Martha IS in the middle = 120 - 96 = 24
Does that help?
Cheers,
Brent
OMG!I can't believe that I
Thanks again for all the help and responses!