Question

An undergraduate class has 24 biology majors and 17 chemistry majors. Eight students must be chosen at random to represent an event organizing committee. What is the probability of choosing exactly two chemistry majors

Answer 1

Answer: 0.19158

Explanation:

Given: An undergraduate class has 24 biology majors and 17 chemistry majors.

Total students needs to be selected = 8

Number of ways to select 8 students out of 41=
`^(41)C_8`

Number of ways to select exactly two chemistry majors (i.e. rest 6 will be biology majors) =
`^(24)C_6* ^(17)C_2`

Required probability =
`(^(24)C_6* ^(17)C_2)/(^(41)C_8)`

`=((24!)/(6!(24-6)!)*(17!)/(2!(17-2)!))/((41!)/(8!(41-8)!))\\\\=(134596*136)/(95548245)\\\\= 0.19158`

The probability of choosing exactly two chemistry majors = 0.19158