Eleven animals of a circus have to placed in eleven cages one in each cage. If 4 of the cages are too small for 6 of the animal, find the number of ways of caging the animals.

Open in App

Solution

Large animals 6 Small animals 5
Large cages 7 Small cages 4
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
$7! \times 5! = 5040 \times 120 = 604800$

Suggest Corrections

Similar questions

Q. 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 ?

Q. 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 :

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 :

10

animals of circus have to be placed in

10

cages with one in each cage. If

3

of the cages are too small for

6

of the animals, then the number of ways of placing the animals in cage is

Q. m distinct animals of a circus have to be placed in m cages, one in each cage. If n(< m) cages are too small to accomoodate p(n < p < m) animals, then the number of ways of putting the animals in to cages are

Join BYJU'S Learning Program

Eleven animals of a circus have to placed in eleven cages one in each cage. If 4 of the cages are too small for 6 of the animal, find the number of ways of caging the animals.

Large animals 6 Small animals 5Large cages 7 Small cages 46 large animals can be caged in 7 large cages in 7P6=7! ways. 5 small animals can be caged in remaining 5 cages (4 small + 1 large) in 5! ways. hence the number of ways is7!×5!=5040×120=604800

Large animals 6 Small animals 5
Large cages 7 Small cages 4
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
$7! \times 5! = 5040 \times 120 = 604800$