Answer: 0.19158
Step-by-step 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= [tex]^{41}C_8[/tex]
Number of ways to select exactly two chemistry majors (i.e. rest 6 will be biology majors) = [tex]^{24}C_6\times ^{17}C_2[/tex]
Required probability = [tex]\dfrac{^{24}C_6\times ^{17}C_2}{^{41}C_8}[/tex]
[tex]=\dfrac{\dfrac{24!}{6!(24-6)!}\times\dfrac{17!}{2!(17-2)!}}{\dfrac{41!}{8!(41-8)!}}\\\\=\dfrac{134596\times136}{95548245}\\\\= 0.19158[/tex]
The probability of choosing exactly two chemistry majors = 0.19158
