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 girl in each team, is 1750, then n is equal to:

Options

A. 24
B. 27
C. 28
D. 25

Answer

D

Explanation

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`