In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is `""^(n-m)P_(r-m) xx ""^("r")P_(m)*`

In the permutations of n things r, taken together, the number of permu

1.	In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is `""^(n-m)P_(r-m) xx ""^("r")P_(m)*`
Answer» False Arrangement of n things, taken r at a time in which m things occur together, we considered these m things as 1 group. Number of object excluding those m objects = (r - m) Now, first we have to arrange (r-m+1) objects. Number of arrangements `=(r-m+1)"!"` and m objects which we consider as 1 group, can be arranged in `m"!"` ways. `therefore` Required number of arrangements `=(r-m+1)"!" xx m"!"`

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In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is `""^(n-m)P_(r-m) xx ""^("r")P_(m)*`

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