Answer:
The probability of selecting 5 female and 2 male students is 0.052.
Step-by-step explanation:
The class comprises of 7 female students and 10 male students.
Total number of students: 17.
Number of female students, 7.
Number of male students, 10.
The probability of an event <em>E</em> is:
![P(E)=\frac{Favorable\ outcomes}{Total\ number\ of] outcomes}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cfrac%7BFavorable%5C%20outcomes%7D%7BTotal%5C%20number%5C%20of%5D%20outcomes%7D)
The number of ways to select 7 students from 17 is:
![N ={17\choose 7}=\frac{17!}{7!(17-7)!}= 19448](https://tex.z-dn.net/?f=N%20%3D%7B17%5Cchoose%207%7D%3D%5Cfrac%7B17%21%7D%7B7%21%2817-7%29%21%7D%3D%2019448)
The number of ways to select 5 female students of 7 females is:
![n(F) ={7\choose 5}=\frac{7!}{5!(7-5)!}= 21](https://tex.z-dn.net/?f=n%28F%29%20%3D%7B7%5Cchoose%205%7D%3D%5Cfrac%7B7%21%7D%7B5%21%287-5%29%21%7D%3D%2021)
The number of ways to select 2 male students of 10 males is:
![n(M) ={10\choose 2}=\frac{10!}{2!(10-2)!}= 45](https://tex.z-dn.net/?f=n%28M%29%20%3D%7B10%5Cchoose%202%7D%3D%5Cfrac%7B10%21%7D%7B2%21%2810-2%29%21%7D%3D%2045)
Compute the probability of selecting 5 female and 2 male students as follows:
P (5 F and 2 M) = [n (F) × n (M)] ÷ N
![=\frac{21\times45}{19448} \\=0.05183\\\approx0.052](https://tex.z-dn.net/?f=%3D%5Cfrac%7B21%5Ctimes45%7D%7B19448%7D%20%5C%5C%3D0.05183%5C%5C%5Capprox0.052)
Thus, the probability of selecting 5 female and 2 male students is 0.052.