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

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

TestHub · Accepted Answer

(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

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Doubts & Discussion

(5)	(n)
Boys	Girls
$2$	$1$
$1$	$2$