Question

URGENT

A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?




A.
5/143


B.

7/143


C.

28/143


D.

30/143

Answer 1

5/13 * 4/12 * 3/11 is our representation, which yields 5/143, A. There is no replacement therefore the amount of available total candidates and available women shrink with each position filled.

Answer 2

`A. (5)/(143)`

Explanation:

Given,

Number of women = 5,

Number of men = 8,

Total persons = 5 + 8 = 13,

∵ Ways of selecting any 3 persons =
`^(13)C_3`

Also, the ways of selecting 3 women =
`^5C_3`

Hence, the probability of selecting 3 women

`=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}`

`=(^5C_3)/(^(13)C_3)`

`=((5!)/(2!3!))/((13!)/(3!10!))`

`=(10)/((13* 12* 11)/(6))`

`=(60)/(13* 12* 11)`

`=(5)/(143)`

Hence, OPTION A is correct.