Permutations And Combinations

Matching exercise

Match the items on the right to the items on the left.

Combination of n different things taken some or all of n things at a time

Combination of n things taken some or all at a time when p of the things are alike of one kind, q of the things are alike and of another kind and r of the things are alike of a third kind

Total number of ways in which n identical items which can be distributed among p persons so that each person may get any number of items

Total number of ways in which n identical items can be distributed among p persons such that each them receive at least one item

If r things are taken at a time out of n distinct things and arranged along a circle, then the number of ways of doing this is

2^{n} - 1

[(p + 1) (q + 1) (r + 1)......] - 1

{}^{n + p - 1}C_{p - 1}

{}^{n - 1}C_{p - 1}

(r - 1)! {}^{n}C_{r}