Question

$10$ men and $5$ women apply for a six-person maths committee. If the six are selected at random, what is the probability that the committee has an equal number of men and women?

• A. $0.18$
• B. $0.24$
• C. $0.31$
• D. $0.35$
• E. $0.40$

Answer 1

Answer: (B)

$0.24$

Total number of ways of selecting $6$ people from $10+5=15$ people will be ${}_6^{15}C=\frac{15!}{6!\times 9!}$

Number of ways of selecting $3$ men from $10$ men and $3$ women from $5$ women is

${}_3^{10}C{\times }_3^{5}C=\frac{10!}{7!\times 3!}\times \frac{5!}{2!\times 3!}$

Probability $=\frac{\frac{10!}{7!\times 3!}\times \frac{5!}{2!\times 3!}}{\frac{15!}{6!\times 9!}}=\frac{240}{1001}=0.24$