Prove that number of permutations of n distinct objects taken r at a time ; when a particular object is never taken in each arrrangement is `(n-1)P_r`

Find the number of permutations of 10 objects, taken 4 at a time.

Find the number of permutations of 7 objects, taken 3 at a time.

Prove that the no.of all permutations of n different objects taken r at a time when a particular object is to be always included in each arrangement is r.(n-1)P_(r-1)

The number of permutations of n different objects taken r(>=3) at a time which include 3 particular objects is

The number of permulations of n different objects taken K at a time , when repetitions are allowed is

The number of permutations of n things taken r at a time if 3 particular things always occur is

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

2.The number of permutations of 8 things taken at a time is 1680, Then r=

The number of permutation of n different objects, taken r at a line, when repetitions are allowed, is …….. .