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

Find the number of permutations of n things, taken r at a time, in which 3 particular things : always occur.

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

Prove that the number of combinations of n things taken r at a time in which p particular things always occur is .^(n-p)C_(r-p)

Prove that the number of combinations of n things taken r at a time in which p particular things always occur is .^(n-p)C_(r-p)

Find the number of permutations of n things, taken r at a time, in which 3 particular things : (i) always occur (ii) will never occur.

Find the number of permutations of n things, taken r at a time, in which 3 particular things : will never occur.

Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are : included .

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

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

In how many of the permutations of 12 things taken 6 at a time will 3 particular things (a) always occur b) never occur ?