Question

What is the probability that two female students will be selected at random to
participate in a certain research project, from a class of seven males and three
female students?

Answer 1

Total number of student in a class$=7+3=10$

Number of ways of selecting two student from 10 student $= \ ^{10}C_2=\frac{10!}{2.(10-2)!}=\frac{10.9}{2}=45$

Number of ways of selecting 2 girls from 3 girls$= \ ^3C_2=\frac{3!}{2.1!}=3$

The probability that both student are girls $=\frac{3}{45}=\frac{1}{15}$