Number of permutations with repetition
Category : JEE Main & Advanced
(1) The number of permutations (arrangements) of \[n\] different objects, taken \[r\] at a time, when each object may occur once, twice, thrice,........upto r times in any arrangement = The number of ways of filling \[r\] places where each place can be filled by any one of \[n\] objects.
The number of permutations = The number of ways of filling \[r\] places \[={{(n)}^{r}}\].
(2) The number of arrangements that can be formed using \[n\] objects out of which \[p\] are identical (and of one kind) \[q\] are identical (and of another kind), \[r\] are identical (and of another kind) and the rest are distinct is \[\frac{n\,!}{p!\,q!r!}\].
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