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

Step-by-step solution

(5) (n) Boys Girls 2 1 1 2 Here total number of ways =   5 C 2 ×   n C 1 + 5 C 1 ×   n C 2 = 1750 ⇒ 10 n + 5 n ( n − 1 ) 2 = 1750 ⇒ n 2 + 3 n − 700 = 0 ⇒ n = − 28 ,   25 n cannot be negative Hence n = 25