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In how many of the permutations of n things taken r at a time

Question

In how many of the permutations of $n$ things taken $r$ at a time will $5$ things (i) always occur, (ii) never occur?

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In how many of the permutations of

n

things taken

r

at a time will

5

things (i) always occur, (ii) never occur?

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Text solutionVerified

(i) Permutations of n different things taken r at a time, when one particular thing always occurs

= r .^{n - 1} P r - 1

(ii) Permutation of n different things taken r at a time when a particular thing never occurs

=^{n - 1} P_{r}

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Question Text	In how many of the permutations of $n$ things taken $r$ at a time will $5$ things (i) always occur, (ii) never occur?
Answer Type	Text solution:1
Upvotes	150