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A group of students comprises of 5 boys ...

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girls in each team, is 1750, then n is equal to:

A

24

B

27

C

28

D

25

Text Solution

Verified by Experts

The correct Answer is:
D
boys `=5, n=` girls
boys `" "` girls
`1" "2`
`2" "1`
`.^(5)C_(1)xx``.^(n)C_(2)+.^(5)C_(2)xx``.^(n)C_(1)=1750`
`(5n(n-1))/2+10n=1750``
`n^(2)-n+4n=700``
`n^(2)=3n=700``
`(n+28)(n-25)=0, n=25`
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