A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many wayscan 4 people be selected from this group of 11? In how many ways can 4 men be selected from the 6 men? Findthe probability that the selected group will consist of all men.
A) $330 ; 15 ; \frac { 1 } { 22 }$
B) $7920 ; 360 ; \frac { 1 } { 22 }$
C) $330 ; 15 ; \frac { 1 } { 15,840 }$
D) $330 ; 15 ; \frac { 1 } { 1,814,400 }$

Question

A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many wayscan 4 people be selected from this group of 11? In how many ways can 4 men be selected from the 6 men? Findthe probability that the selected group will consist of all men. 
A) $330 ; 15 ; \frac { 1 } { 22 }$
B) $7920 ; 360 ; \frac { 1 } { 22 }$
C) $330 ; 15 ; \frac { 1 } { 15,840 }$
D) $330 ; 15 ; \frac { 1 } { 1,814,400 }$

Quizplus · Accepted Answer

The total number of ways to select 4 people from 11 is calculated using the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items, $k$ is the number of items to choose, and "!" denotes factorial. For selecting 4 people from 11, it is $C(11, 4) = \frac{11!}{4!(11-4)!} = 330$. For selecting 4 men from 6, it is $C(6, 4) = \frac{6!}{4!(6-4)!} = 15$. The probability of selecting 4 men out of the total selections is the ratio of the two, $\frac{15}{330} = \frac{1}{22}$.

A Group Consists of 6 Men and 5 Women 330;15;122330 ; 15 ; \frac { 1 } { 22 }330;15;221​

A Group Consists of 6 Men and 5 Women $330 ; 15 ; \frac { 1 } { 22 }$