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

Prove that the no. of permutations of n different objects taken r at a time in which two specified objects always occur together 2!(r-1) (n-2)P_(r-2)

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times.

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)

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

There are 4n things of which n are alike and the rest different. Find the number of permutations of 4n things taken 2n at a time, each permutation containing the n like things.

Show that the total number of permutations of n different things taken not more than r at a time, when each thing may be repated any number of times is (n(n^(r)-1))/((n-1)) .