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m distinct animals of a circus have to be placed in m cages, o

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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

(^{m - n} P_{p}) (^{m - p} P_{m - p})

^{m - n} C_{p}

(^{m - n} C_{p}) (^{m - p} C_{m - p})

None

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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

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Text solutionVerified

Number of ways of arranging p big animals into m n big cages

=^{m - n} p_{p}

.
Now remaining animals can be arranged in any cage in

^{n - p} P_{m - p}

ways

∴

Desired number of ways

=^{m - n} P_{p} \times^{m - p} P_{m - p}

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Question Text	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
Answer Type	Text solution:1
Upvotes	151

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

Text solutionVerified

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