Question

# Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals, the number of ways of caging the animals is-

^{7}P_{6}. 5!
^{6}P_{4}. 7!
^{11}C_{4}. 7!
- None of these

^{7}P_{6}. 5!^{6}P_{4}. 7!^{11}C_{4}. 7!Hint:

## From the statement we can conclude that :There are 6 large animals and 5 small animals also there are 7 large cages and 4 small cages. Arrange the animals accordingly.

## The correct answer is: ^{7}P_{6}. 5!

### We have been given that eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals

## From the above statement we can conclude that :There are 6 large animals and 5 small animals also there are 7 large cages and 4 small cages.

## 6 large animals can be caged in 7 large cages in ways.

## 5 small animals can be caged in remaining 5 cages (4 small + 1 large) in 5! ways.

## Thus, the number of ways of caging the animals is =

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