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

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

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

If the number of permutations of n different things taken 4 at a time in which one particular thing does not occur is equal to that in which it does occur,find n .

Statement-1: Number of permutations of 'n' dissimilar things taken 'n' at a time is n!. Statement-2: If n(A)=n(B)=n, then the total number of functions from A to B are n!.

Assertion (A) : The number of selections of 20 distinct things taken 8 at a time is same as that taken 12 at a time Reason (R): C(n, r) = C(n, s), if n = r + s