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 of the animals, then find the number of the ways of caging all the animals.

Answer 1

Let the 6 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, by the fundamental theorem, the required number of ways is `.^(7)P_(6)xx5!=604800`.