A committee of 6 people, which must contain at least 4 men and at least 1 woman,

Question

A committee of 6 people, which must contain at least 4 men and at least 1 woman, is to be chosen from 10 men and 9 women. (i) Find the number of possible committees that can be chosen. (ii) Find the probability that one particular man, Anil, and one particular woman, Stacy, are both on the committee. (iii) Find the number of possible committees that include either Anil or Stacy but not both. (iv) The committee that is chosen consists of 4 men and 2 women. They line up randomly for refreshments. Find the probability that the two women are not next to each other.

Explanation / Answer

2)

i)

number of possible committees

= 4 men and 2 women + 5 men and 1 women

= 10C4 * 9C2 + 10C5 * 9C1

= 9828

ii)

so , 2 people are fixed , so remaining 4 should be chosen from 9 men and 8 women

=>

number of possible committees = 17C4 = 2380

iii)

number of possible committees = 18C5 + 18C5 = 2 * 18C5 = 17136

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