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

Question

Aicharya · Accepted Answer

(5) (n) Boys Girls 2 1 1 2 Here total number of ways = &#160; 5 C 2 &#215; &#160; n C 1 + 5 C 1 &#215; &#160; n C 2 = 1750 &#8658; 10 n + 5 n ( n &#8722; 1 ) 2 = 1750 &#8658; n 2 + 3 n &#8722; 700 = 0 &#8658; n = &#8722; 28 , &#160; 25 n cannot be negative Hence n = 25

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students…

Solution

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