Consider a class with 10 boys and 8 girls a In how many way

Consider a class with 10 boys and 8 girls .

a) In how many ways can a committee of ten consisting of 4 boys and 6 girls be chosen?

b) How many of the possible ways a committee of five can be chosen at random from the class consists at least 3 girls ?

Here, a committe does no require order, so we use combinations.

Thus, there are 10C4 = 210 ways to select 4 boys.

Also, there are 8C6 = 28 ways to select 6 girls.

Thus, selecting 4 boys and 6 girls would have

N = 210*28 = 5880 ways [ANSWER]

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There are 3 cases here:

1. 3 girls, 2 boys
2. 4 girls, 1 boy
5. 5 girls

Case 1:

N1 = (8C3)(10C2) = 2520

Case 2:

N2 = (8C4)(10C1) = 700

Case 3:

N3 = (8C5)(10C0) = 56

Thus, totalling,

N1 + N2 + N3 = total number of ways = 3276 [ANSWER]