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?

Question

Gabriella Khan

Mathematics

8 June, 10:29

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?

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Answers (1)

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Todd · Answer 1

0.21 or 21/100

Step-by-step 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