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 :

^{11} C_{6} \times 4!

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^{11} C_{6} \times 5!

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7! \times 4!

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7! \times 5!

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Solution

The correct option is D $7! \times 5!$
$6$ large animals can be caged in $7$ large cages in $7!$ 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 $= 7! \times 5!$

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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 big animals, then the number of the ways of caging all the animals is :

The correct option is D 7!×5! 6 large animals can be caged in 7 large cages in 7! 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!×5!

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 :

The correct option is D $7! \times 5!$
$6$ large animals can be caged in $7$ large cages in $7!$ 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 $= 7! \times 5!$