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-
- 7P6. 5!
- 6P4. 7!
- 11C4. 7!
- None of these
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: 7P6. 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 = 
ways.Related Questions to study
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It is important to note that we have used a fact that 
= 
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It is important to note that we have used a fact that = . This can be understood as we know that = and = . So, substituting this we have = .
A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?
Whenever we face such types of problems the key point is to make special arrangements for the people who are in need of it, then arrange the remaining. Now combination comes with permutation as there are possibilities of these 8 people sitting on one side to rearrange. Thus this concept into consideration, to get through the answer.
A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?
Whenever we face such types of problems the key point is to make special arrangements for the people who are in need of it, then arrange the remaining. Now combination comes with permutation as there are possibilities of these 8 people sitting on one side to rearrange. Thus this concept into consideration, to get through the answer.
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