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There are 10 men and 7 women working as supervisors in a company. The company has recently decided to form a committee to represent all the employees. The committee has to consist of 3 members, all of whom must be supervisors. The members will be President, General Secretary and Coordinator respectively. Answer the following questions based on this information. How many ways can the committee be formed if it must have at least one man and at least one woman?

which one is correct?

a 7p1*10p1*17p1+7p2*10p1*17p0+7p1*10p2*17p0

b.7p1*10p2+7p2*10p1

Ishrak Alaxander Hasin
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1 Answers1

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Since there must be at least one man and woman, the committee must have either $1$ man and $2$ women, or $2$ men and $1$ woman.

Take the first choice. We have ten choices for the man, and he can fill either of the three positions. Then, given a choice of a man and his position, we have seven choices for the women, who must fill two positions, and each pair of women could take either position.

So our calculation for this case is ${10 \choose 1} * 3 * {7 \choose 2} * 2 = 1260$

Now look at the other case: $2$ men and $1$ woman. This runs relatively parallel to the case above, and our calculation is ${7 \choose 1} * 3 * {10 \choose 2} * 2 = 1890$.

So the total number of ways the committee can be formed is $1260 + 1890 = 3150$

elDin0
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