Question

A school debate team has 4 girls and 6 boys. A total of 3 of the team members will be chosen to participate in the district debate. What is the probability that 1 girl and 2 boys will be selected?

Answer 1

`P=\frac{\binom{4}{1}\binom{6}{2}}{\binom{6+4}{3}}=(4*(6*5/2))/(10*9*8/(3*2))=1/2`

Answer 2

The number of all possible 3-person groups

`{10 \choose 3}=(10!)/(3!7!)=(8\cdot9\cdot10)/(6)=120`

The number of all possible groups consisting of 1 girl and 2 boys

`4\cdot{6\choose 2}=4\cdot(6!)/(2!4!)=4\cdot(5\cdot6)/(2)=60`

The probability is
`(60)/(120)=(1)/(2)`