Indian Institute of Foreign Trade 2016 Solved Paper

(d) 5 students out of 4 boys and y girls can be chosen in 2 ways.
There are two conditions:
(i) 3 Boys & 2 Girls =4C3×yC2
(ii) 4 Boys & 1 Girl=4C4×yC1
Since only boys are given a ball, thus
Total balls given to 3 boys each in 1‌st case + Total balls given to 4 boys each in 2‌nd case = 368
⇒3×‌4C3×‌yC2+4×‌4C4×‌yC1=368
⇒3×4×

y(y−1)

2

+4×1×y=368
⇒6y(y−1)+4y=368
⇒6y2−6y+4y=368
⇒3y2−y‌‌‌‌‌‌‌‌‌‌=184
⇒3y2−y−184=0
on solving this. then, y = 8.