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

Question

Quizplus · Accepted Answer

The probability of selecting three parents and three teachers is the number of ways to select three parents from eight parents multiplied by the number of ways to select three teachers from four teachers, divided by the total number of ways to select six people from twelve people.The number of ways to select three parents from eight parents is $\binom{8}{3} = 56$.The number of ways to select three teachers from four teachers is $\binom{4}{3} = 4$.The total number of ways to select six people from twelve people is $\binom{12}{6} = 924$.Therefore, the probability of selecting three parents and three teachers is $\frac{56 \times 4}{924} = \frac{2}{33}$.

Compute Probabilities Involving Permutations and Combinations -A Committee Consisting of 6

Compute Probabilities Involving Permutations and Combinations
-A Committee Consisting of 6