The number of combinations of n different things taken r at a time in which p particular things always occur is -

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)

The number of permutations of n different things taken r at a time in which 4 particular things never occur is -

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 .

The number of combinations of n different of n different things taken r at a time in which p particular things never occur is -

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 3 particular things : always occur.

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 3 particular things : (i) always occur (ii) will never occur.