A group of 20 students consists of 12 boys and 8 girls. A committee of 5 students is to be selected randomly from this group. What is the probability that the committee has more boys than girls?
Show answer & explanation
Correct answer: B
Explanation
Total students = 20
Boys = 12
Girls = 8
Total ways to form a committee of 5 students -
²⁰C₅ = 15504
Scenarios with more boys -
3 boys, 2 girls
4 boys, 1 girl
5 boys, 0 girls
Favorable ways -
3 boys, 2 girls -
¹²C₃ × ⁸C₂
= 220 × 28 = 6160
4 boys, 1 girl -
¹²C₄ × ⁸C₁
= 495 × 8 = 3960
5 boys -
¹²C₅ × ⁸C₀
= 792 × 1 = 792
Total favorable ways -
6160 + 3960 + 792 = 10912
Probability = 10912 / 15504 ≈ 0.704 ≈ 0.70