A committee consisting of 6 people is to be selected from eight parents and four teachers. Find the probabilityof selecting three parents and three teachers.
A) $\frac { 8 } { 33 }$
B) $\frac { 2 } { 33 }$
C) $\frac { 100 } { 231 }$
D) $\frac { 10 } { 11 }$

Question

A committee consisting of 6 people is to be selected from eight parents and four teachers. Find the probabilityof selecting three parents and three teachers. 
A) $\frac { 8 } { 33 }$
B) $\frac { 2 } { 33 }$
C) $\frac { 100 } { 231 }$
D) $\frac { 10 } { 11 }$

Quizplus · Accepted Answer

The probability of selecting three parents from eight parents is $\frac { 8 } { 12 }\times \frac { 7 } { 11 }\times \frac { 6 } { 10 }$ = $\frac { 336 } { 1320 }$The probability of selecting three teachers from four teachers is $\frac { 4 } { 12 }\times \frac { 3 } { 11 }\times \frac { 2 } { 10 }$ = $\frac { 24 } { 1320 }$Therefore, the probability of selecting three parents and three teachers is $\frac { 336 } { 1320 }\times \frac { 24 } { 1320 }$ = $\frac { 8064 } { 1742400 }$ = $\frac { 8 } { 33 }$

A Committee Consisting of 6 People Is to Be Selected 833\frac { 8 } { 33 }338​

A Committee Consisting of 6 People Is to Be Selected $\frac { 8 } { 33 }$