Question

3 female students and 7 male students are nominated for scholarships.  All 10 students are equally qualified and equally likely to be chosen.  You may assume any person can receive a maximum of one scholarship.  You are awarding a total of 3 scholarships.  What is the probability that all the scholarships are given to females?  ​

Answer 1

0.21 or 21/100

Explanation:

the chance of a female student getting a scholarship is 7/10. now that student already has a scholarship so now there are 9 students. the probability of the next female getting a scholarship is 6/9. and then the next is 5/8

7/10 x 6/9 x 5/8 = 21/100 or 0.21