First slide

Permutations

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 the number of ways of caging the animals i

Moderate

A

304800
B

504800
C

604800
D

None of these

Solution

6 large animals can be caged in 7 large cages in $^{7} P_{6} = 7!$ ways.
5 small animals can be caged in remaining 5 cages (4 small + 1 large) in 5! ways.
Hence, the number of ways is 7! × 5! = 5040 × 120 = 604800

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