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Permutation: n Different Things Taken r at a Time

Find the numb...

Question

Find the number of permutations of n different things taken r at a time such that two specified things occur together ?

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Solution

There are x things

Two specific things are to occur together, so remaining things are (r - 2).

Now, number of ways to arrange (r - 2) things out of $(n - 2) =^{(n - 2)} P_{(r - 2)}$ .

Two things can be arranged is (r - 1) ways. and these two can be placed in 2 ways.

Therefore,

Required number of ways

$= 2 (r - 1)^{(n - 2)} P_{(r - 2)}$

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Permutation: n Different Things Taken r at a Time

Standard XII Mathematics

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