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Probability Question

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by Leo2008 » Sat Mar 22, 2008 2:36 pm
Can someone solve this with the explanation ?

A company has received 28 applications, 7 of which are from women to fill 15 vacancies. Of these 15 vacancies, 4 are specialized jobs and have to be filled only by women. In how many ways can the company fill the vacancies ?

Can someone explain what's wrong with the solution (7C4)*(24C11)


The correct answer is

(7C7*21C8) + (7C6*21C9) + (7C5*21C10) + (7C4*21C11)
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Re: Probability Question

by camitava » Sat Mar 22, 2008 5:27 pm
Leo2008 wrote:Can someone solve this with the explanation ?

A company has received 28 applications, 7 of which are from women to fill 15 vacancies. Of these 15 vacancies, 4 are specialized jobs and have to be filled only by women. In how many ways can the company fill the vacancies ?

Can someone explain what's wrong with the solution (7C4)*(24C11)


The correct answer is

(7C7*21C8) + (7C6*21C9) + (7C5*21C10) + (7C4*21C11)
Your attempt - (7C4)*(24C11) - is not the answer to chose. Now look at the explanation (according to me) -
7 women 4 jobs so comb = 7C4.
21 men 11 jobs so comb = 21C11 but not 24C11. Now this response has become very narrow. What if the no of women selected for the job is 5, 6 or 7? Ans these are the situations that have been covered by the answer u provided.
Correct me If I am wrong


Regards,

Amitava
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