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Question
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
Options
rn
nr
`(n!)/((n - r)!)`
`(n!)/((n + r)!)`
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Solution
The number of permutation of n different things taken r at a time, when the repetition is allowed is nr.
Explanation:
The correct answer is nr because when repetition is allowed, each of the r positions can be filled by any one of the n different objects. Thus, the total number of possible permutations is n × n × ... × n = nr.
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