# Combinations

Each of the selections that can be made with a given number of objects taken some or all of them at a time is called a Combination.

Result-1 : To find the number of combinations of 'n' dissimilar things taken 'r' at a time :

Thus, the total number of combinations of 'n' dissimilar things taken 'r' at a time is ^{n}C_{r}.

The number of combinations of 'n' dissimilar things taken all at a time = ^{n}C_{n} = 1.

**Result****-2 : To find the number of Combinations of 'n' different things taking some or all at a time :**

**Result****-3 : The number of selections of some or all out of (p + q + r + ..... ) things out of which p are alike of one kind, q - alike of second kind and so on :**

The total number of required ways

= (p + 1) (q + 1) (r + 1) ...... â€“ 1

**Result****-4 : The number of selections of one or more things from 'p' identical things of one kind, 'q' identical things of a second kind, 'r' identical things of a third kind and 'n' different things**

The total number of required ways

= (p + 1) (q + 1) (r + 1) 2^{n} â€“ 1