There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?a)10420b)11c)11760d)None of theseCorrect answer is option 'C'. Can you explain this answer?

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Answer

To form a committee of 5 men and 6 women from a group of 8 men and 10 women, we need to calculate the number of ways this can be done.

We can solve this problem using the concept of combinations.

The number of ways to choose 5 men from a group of 8 is given by the combination formula:

C(8, 5) = 8! / (5!(8-5)!) = 8! / (5!3!) = (8 * 7 * 6) / (3 * 2 * 1) = 56

Similarly, the number of ways to choose 6 women from a group of 10 is given by:

C(10, 6) = 10! / (6!(10-6)!) = 10! / (6!4!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210

To find the total number of ways to form the committee, we multiply these two values together:

Total number of ways = C(8, 5) * C(10, 6) = 56 * 210 = 11,760

Therefore, the committee can be formed in 11,760 different ways.

Hence, the correct answer is option C.

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