The no. of all permutation of n distinct things taken all at a time is `n!`

Notation + theorem :- Let r and n be the positive integers such that 1<=r<=n. Then no.of all permutations of n distinct things taken r at a time is given by (n)(n-1)(n-2)....(n-(r-1))

Let P_(n) denote the number of permutation of n distinct things taken all at a time and x_(n)=^(n+5)C_(4)-((143)/(96))((P_(n+5))/(P_(n+3))) (where n in N .The possible value of n for which x_(n) is negative,can be

Show that the numbers of permutations of n different things taken all at a time in which m particular things are never together is (n-m)!(n-m+1)! .

theorem: The no.of all combinations of n distinct objects taken r at a time is given by nC_(-)r=n!/(n-r)!.r! )

If P(n, n) denotes the number of permutations of n different things taken all at a time then P(n, n) is also identical to , where 0 le r le n

The number of permutations of n different things taken r at a time in which 4 particular things never occur is -

Find the number of permutations of n different things taken r at a time such that two specific things occur together?

Find the number of permutations of n different things taken r at a time such that 3 specific things occur together ?