Question

A committee of six students is to be chosen from a class of 38 to bring a petition to the admisitration.

A.) How many such committees can be chosen?

B.) If there are 20 males and 18 females in the class, what is the probability that 2 females will be chosen?

C.) If there are 20 males and 18 females in the class, what is the probability that no more than 2 females will be chosen?

Answer 1

A) 6 to be choosen from 38

$\binom{38}{6}=\frac{38!}{6!*(38-6)!}=\frac{38!}{6!*32!}=2760681$

2760681 such committees can be choosen

B) 20 males, 18 females and to find probability that 2 out of 6 are females

$Probability=\frac{\binom{18}{2}\binom{20}{4}}{\binom{38}{6}}=\frac{153*4845}{2760681}= 0.2685$

C. No more than 2 females will be choosen.i.e. less than or equal to 2 females will be choosen

$Probability=\frac{\binom{20}{6}}{\binom{38}{6}}+\frac{\binom{20}{5}\binom{18}{1}}{\binom{36}{6}}+\frac{\binom{18}{2}\binom{20}{4}}{\binom{38}{6}}=\frac{38760}{2760681}+\frac{15504*18}{2760681}+\frac{153*4845}{2760681}= 0.3836$