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, find the number of ways of caging the animals.___

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Solution

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

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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, find the number of ways of caging the animals.___

Large animals 6 Small animals 5 Large cages 7 Small cages 4 6 large animals can be cages in 7 large cages in 7p6=7!. 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.

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