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 ?

Solution

a. ¹⁰C4 x ⁸C6

= 10!/4!x6! x 8!/2!x6!

= 210 x 28

=5880

b. all 5 girls( ⁸C5) + 4 girls and 1 boy (⁸C4 x ¹⁰C1) + 3 girls and 2 boys (⁸C3 x ¹⁰C2)

56 + (70 x 10) + (56 x 45)

56 + 700 + 2520

3276