Question

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 1

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"!"`