NIMCET 2018 — Mathematics PYQ

Concept:

Number of ways of arranging n identical items in r ways is given ${}_r^{n}P=\frac{n!}{(n-r)!}$

CASTOOO COM

Calculation

Total number of balls are 9, and total number of boxes are also 9

5 balls cannot fit into 3 small boxes, this means that these 5 balls can only fit into 6 remaining balls

so number of ways of arranging 5 balls in 6 boxes is:

$${}_5^{6}P=\frac{(6)!}{(6-5)!}$$
=6!

=720 ways

Now, remaining 4 balls fits into 4 remaining boxes.
Number of ways of arranging 4 balls in 4 boxes is 4!=24 ways
So total number of ways is $720\times 24=17280$