A group of students comprises of 5 boys and n girls.

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:

Accepted Answer

Given that 5 Boy, n girls.

(1B, 2G) + (2B, 1G)

$${}^5{C_1}.{}^n{C_2} + {}^5{C_2}.{}^n{C_1} = 1750$$

$$ \Rightarrow 5.{{n\left( {n - 1} \right)} \over 2} + 10.n = 1750$$

$$ \Rightarrow {{n\left( {n - 1} \right)} \over 2} + 2n = 350$$

$$ \Rightarrow {n^2} - n + 4n = 700$$

$$ \Rightarrow {n^2} + 3n - 700 = 0$$

$$ \Rightarrow (n + 28)(n - 25) = 0$$

$$ \Rightarrow  n = 25, -28$$

Solutions · 1