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Standard XII

Mathematics

Permutation: n Different Things Taken r at a Time

m distinct an...

Question

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})

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^{m - n} C_{p}

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

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None

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Solution

The correct option is B $(^{m - n} P_{p}) (^{m - p} P_{m - p})$
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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Similar questions

Q. Assertion :In a zoo,

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distinct animals of a circus have to be placed is

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cages, one in each cage. If

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then the number of ways of putting the animals into cages is

(\begin{matrix} m - n p \end{matrix}) (\begin{matrix} m - p m - p \end{matrix})

Reason: If a work can be done by

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animals of circus have to be placed in

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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 $6$ big animals, then the number of the ways of caging all the animals is :

Q. Eleven animals of a circus have to be placed in eleven cages (one in each cage). If

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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

The correct option is B (m−nPp)(m−pPm−p)Number of ways of arranging p big animals into m n big cages =m−npp.Now remaining animals can be arranged in any cage in n−pPm−p ways ∴ Desired number of ways =m−nPp×m−pPm−p

The correct option is B $(^{m - n} P_{p}) (^{m - p} P_{m - p})$
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 $=^{m - n} P_{p} \times^{m - p} P_{m - p}$