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`

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

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

The number of permutations of 'n' different objects taken r at a time, when a particular element always occur in each arrangement, is

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)

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 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 things taken r at a time in which two particular things : never occur.

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