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

The number of circular permutations of n different objects is

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

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)

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 .

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 things taken r at a time in which 4 particular things never occur is -

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)

The number of permutations of n different things taking r at a time when 3 particular things are to be included is a. \ ^(n-3)P_(r-3) b. \ ^(n-3)P_r c. \ ^n P_(r-3) d. \ r !^(n-3)C_(r-3)