Question

The number of permutations of n dissimilar things taken 'r' at a time, in which a particular thing always occur is ____

A
(n1)P(r1)
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B
(r) (n1)P(r1)
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C
(r) (n1)Pr
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D
(r!) (n1)P(r1)
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Solution

The correct option is B (r) (n−1)P(r−1)Here we have "n" things and we have to find out the permutation of "r" things take at a time such that one particular thing is always coming. Take an example, you have letters A to Z. Here you have to choose 10 letters such that R always comes i.e. R is fixed, so we just have 25 letters and we have to choose 9 out of them as we have already chosen one (R).Similarly, here we have to chose (r−1) from (n−1) which can be done in (n−1)C(r−1). Now we have r selection which can be arranged in r! ways (n−1)C(r−1)×r!=(r)×(n−1)P(r−1).

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