Question

# 9. A committee of size 4 is to be formed from a group of 5 men...

9. A committee of size 4 is to be formed from a group of 5 men and 5 women. How many committees are possible if

a. there is no restriction on who can serve on the committee?

b. the committee must have at least 1 woman?

Given size of committee is 4

5 men

5 women

a)   there is no restriction on who can serve on the committee

10C4 = 10! / 6! * 4! = 210

b)

Committee consisting of at least 1 woman means

Selecting 1 women and 4 men + Selecting 2 women and 3 men + Selecting 3 women and 2 men + Selecting 4 women and 1 men + Selecting 5 women

= 5C1 *5C3 +5C2 *5C2 +5C3*5C1 + 5C4
= 50 + 100 + 50 + 5 = 205

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