Question

There are 4 boys and 8 girls on a debate team. The coach randomly chooses 3 of the students to participate in a competition. What is the probability that the coach chooses all girls ? Leave your answer as a simplified fraction

Answer 1

Without replacement, the probability of choosing 3 girls is (according to the question)

`P(3girls)=(_8C_3)/(12C_3)=((8!)/(3!(8-3)!))/((12!)/(3!(12-3)!))`

Simplifying,

`\Rightarrow P(3girls)=(8!*9!)/(12!*5!)=(8*7*6)/(12*11*10)=(336)/(1320)=(14)/(55)`

Type 336/1320 first; then, 14/55