KVPY Sample Paper KVPY Stream-SX Model Paper-30

Number of ways in which 6 different toys can be distributed In 5 children. If exactly one child does not get any toy

A) 1200

B) 2400

C) 240

D) 300

Correct Answer: A

Solution :

\[^{5}{{C}_{1}}\] = number of ways to select a child who does not get any toy 5 toys to be distributed to 4 children, so that each gets at least one.

Toys	\[{{C}_{1}}\]	\[{{C}_{2}}\]	\[{{C}_{3}}\]	\[{{C}_{4}}\]
5 \[\equiv \]	1	1	1	2

Number of ways = \[\frac{5!}{3!2!}\times 4!{{\times }^{5}}{{C}_{1}}=1200\]