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Standard XII

Mathematics

Permutation: n Different Things Taken r at a Time

What is the n...

Question

What is the number of permutations of $n$ objects, where $p_{1}$ object are of one kind, $p_{2}$ are of second kind, .... $p_{k}$ are of $k^{t h}$ kind and the rest, if any, are of different kind?

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Solution

Here $p_{1}, p_{2} . . . . . . . ., p_{k}$ are of different kind
Hence we can find number or permutations by formula of permutation when the objects are not distict kind
$∴$ The number of permutations of n objects $= \frac{n!}{p_{1}! p_{2}! . . . p_{k}!}$

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What is the number of permutations of n objects, where p1 object are of one kind, p2 are of second kind, ....pk are of kth kind and the rest, if any, are of different kind?

Here p1,p2........,pk are of different kind Hence we can find number or permutations by formula of permutation when the objects are not distict kind∴ The number of permutations of n objects=n!p1!p2!...pk!

What is the number of permutations of $n$ objects, where $p_{1}$ object are of one kind, $p_{2}$ are of second kind, .... $p_{k}$ are of $k^{t h}$ kind and the rest, if any, are of different kind?

Here $p_{1}, p_{2} . . . . . . . ., p_{k}$ are of different kind
Hence we can find number or permutations by formula of permutation when the objects are not distict kind
$∴$ The number of permutations of n objects $= \frac{n!}{p_{1}! p_{2}! . . . p_{k}!}$