Question

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

Answer 1

Correct Answer - C
It is given that the group of students comprises of 5 boys and n girls. The number of ways, in which a team of 3 students can be selected from this group such that each team consists of at least one boy and at least one girls, is = (number of ways selecting one boy and 2 girls) + (number of ways selecting two boys and 1 girl)
`= (""^(5)C_(1) xx ""^(n)C_(2)) (""^(5)C_(2) xx ""^(n)C_(1)) = 1750` [given]
`rArr " " (5 xx (n(n - 1))/(2)) + ((5 xx 4)/(2) XX n) = 1750`
`rArr n(n - 1) + 4n = 2/5 xx 1750 rArr n^(2) + 3n = 2 xx 350`
`rArr n^(2) + 3n - 700 = 0`