Question

The Board of Directors at Smallville National Bank consists of 12 members - 9 male and 3 female. A revised mortgage policy manual is planned and a committee of 3 Board members will prepare the manual and be selected randomly. a. What is the probability that all committee members will be male

Answer 1

`(21)/(55)`

Explanation:

Let:

A = any 3 board members

B = 3 male board members

`n(A)=_(12)C_3`

`=(12!)/(3!9!)`

`=(12*11*10)/(3*2*1)`

`=220`

`n(B)=_9C_3`

`=(9!)/(3!6!)`

`=(9*8*7)/(3*2*1)`

`=84`

`P(B|A)=(n(B))/(n(A))`

`=(84)/(220)`

`=(21)/(55)`