Question

A committee of $6$ teachers is to be formed from $5$ male teachers and $8$ female teachers. If the committee is selected at random, what is the probability that it has an equal number of male and female teachers?

• A. $1/10$
• B. $140/429$
• C. $150/429$
• D. $160/429$
• E. $170/429$

Answer 1

Answer: (B)

$140/429$

• The number of ways of selecting $6$ teachers from $5$ males and $8$ female teachers is ${{}^{5}C}_5{{}^{8}C}_1+{{}^{5}C}_4{{}^{8}C}_2+{{}^{5}C}_3{{}^{8}C}_3+{{}^{5}C}_2{{}^{8}C}_4+{{}^{5}C}_1{{}^{8}C}_5+{{}^{5}C}_0{{}^{8}C}_6=429$
• The number of ways of selecting such that males and females are equal is ${{}^{5}C}_3{{}^{8}C}_3=140$
• So the probability is $140/429$