HannahRBaldt
contestada

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

Respuesta :

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:

[tex]A. \frac{5}{143}[/tex]

Step-by-step explanation:

Given,

Number of women = 5,

Number of men = 8,

Total persons = 5 + 8 = 13,

∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]

Also, the ways of selecting 3 women = [tex]^5C_3[/tex]

Hence, the probability of selecting 3 women

[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]

[tex]=\frac{^5C_3}{^{13}C_3}[/tex]

[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]

[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]

[tex]=\frac{60}{13\times 12\times 11}[/tex]

[tex]=\frac{5}{143}[/tex]

Hence, OPTION A is correct.