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

Find the number of permutations of n different things taken r at a time such that 3 specific things occur together ?

The number of circular permutations of 8 things taken 4 at a time is

The number of circular permutations of 8 things taken 4 at a time is

Find the number of permutations of n different things taken r at time so that m(ltr) particular things will never occur.

Find the number of permutations of n different things taken r at time so that m(ltr) particular things will always occur

Find the number of permutations of n things taken r at a time in which two particular things : always occur.

Find the number of permutations of n things taken r at a time in which two particular things : never occur.

The number of circular permutation of 8 things taken 4 at a time 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 20 things taken 5 at a time so that one particular thing will always occur