Question

$10$ animals of circus have to be placed in $10$ cages with one in each cage. If $3$ of the cages are too small for $6$ of the animals, then the number of ways of placing the animals in cage is

• A. $30240$
• B. $120960$
• C. $168$
• D. $103680$

Answer 1

The correct option is A $30240$

$6$ animals to be arranged in $7$ large cages

${=}^7{C}_6\times 6!$

$=7!$

$4$ animals in $4$ cages$=4!$

$\therefore 7!\times 4!=30240$