Question

A teacher-student committee consisting of 4 people is to be formed from 5 teachers and 20 students. Find the probability that the committee will consist of at least one student

Answer 1

Answer:

0.11424901185

Step-by-step explanation:

$=\frac{n(combination \ with \ least \ 1 \ student)}{n(Total \ possible \ combinations )}\\= \frac{n(1 \ student \ and \ 3 \ teachers) + n(2 \ S \ and \ 2 \ T) + n(3 \ S \ and \ 1 \ T)+ n(4S,0T)}{n(total)}$

$=\frac{\binom{4}{1} \binom{20}{3} + \binom{4}{2} \binom{20}{2} +\binom{4}{3}\binom{20}{1} + \binom{4}{4}\binom{20}{0}}{\binom{25}{4}}$

$=\frac{(4)(1140)+(6)(190)+(4)(20)+1}{(100)(506)}\\=0.11424901185$