Question

A class contains 10 students with 6 boys and 4 girls. Find the number of ways: i. A 4 member committee can be selected from the students. ii. A 4 member committee with 2 boys and 2 girls can be selected from the students. iii. A 4 member committee at least 3 boys can be selected from the students.

Answer 1

i.

$$\dbinom{10}{4}=210$$

ii.

$$\dbinom{6}{2}\dbinom{4}{2}=15(6)=90$$

iii.

$$\dbinom{6}{3}\dbinom{4}{1}+\dbinom{6}{4}\dbinom{4}{0}=20(4)+15(1)=95$$