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 is ?

304800

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504800

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604800

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Solution

The correct option is C

604800

Five smaller animals can fit in the four cages
so number of ways of choosing $=^5C_4$
now number of permutations $=^5C_4*4$
now the remaining seven cages have to be filled with seven animals
so number of permutations=$7^C_7*7!$
so total $=5^C_4*4*7^C_7*7!=604800$

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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, then the number of ways of caging the animals is ?

The correct option is C 604800Five smaller animals can fit in the four cages so number of ways of choosing $=^5C_4$ now number of permutations $=^5C_4*4$ now the remaining seven cages have to be filled with seven animals so number of permutations=$7^C_7*7!$ so total $=5^C_4*4*7^C_7*7!=604800$

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 is ?

The correct option is C $604800$
Five smaller animals can fit in the four cages so number of ways of choosing $=^5C_4$ now number of permutations $=^5C_44$ now the remaining seven cages have to be filled with seven animals so number of permutations=$7^C_77!$ so total $=5^C_447^C_7*7!=604800$