Question

In a group of 20 boys and 14 girls, three people are chosen at random. What is the probability that 1 girl and 2 boys are selected

Answer 1

Answer:
`(665)/(1496)`

Explanation:

Given : In a group , there are 20 boys and 14 girls.

Total people = 20+14=34

Number of ways to choose 3 people out of 34 =
`^(34)C_3`

Number of ways to choose 1 girl and 2 boys =
`^(14)C_1*^(20)C_2`

The probability that 1 girl and 2 boys are selected =
`(^(14)C_1* ^(20)C_2)/(^(34)C_3)`

`(14*(20!)/(2!18!))/((34!)/(3!31!))\ \ \ [^nC_r=(n!)/(r!(n-r)!)]\\\\=(14*(20*19)/(2))/((34*33*32*31!)/(3*2\tims3!))\\\\=(665)/(1496)`

Hence, required probability =
`(665)/(1496)`