Question

Eleven animals of a circus have to be placed in eleven cages (one in each cage). If $4$ of the cages are too small for $6$ big animals, then the number of the ways of caging all the animals is :

• A. ${}^{11}{P}_6\times 4!$
• B. ${}^{11}{P}_6\times 5!$
• C. ${}^7{P}_6\times 4!$
• D. ${}^7{P}_6\times 5!$

Answer 1

The correct option is D ${}^7{P}_6\times 5!$

Let the $6$ big animals be placed in $7$ of larger cages. This can be done in ${}^7{P}_6$ ways.
In each of these ways, one larger cage is left vacant.
The remaining five animals can be placed in the remaining five cages in $5!$ ways.
Hence, the required number of ways $={}^7{P}_6\times 5!$