## Permutations and Combinations-algebra tutors

### Permutations and Combinations(part-2)

In my previous post, we discussed the fundamental principle of counting and various methods of permutations. In this post, I shall discuss combinations in details.

**Meaning of Combination-** If we are given a set of objects and we want to select a few objects out of this set, then we can do it by many different ways. These ways are known as combinations.

**Example-** If we are given three balls marked as B, W and R and we want to select two balls then we can select like this- BW, BR, WR.

These are known as the combination of this selection.

**Combination of n different objects taken r at a time when repetition is not allowed**– If repetition is not allowed the number of ways of selecting r objects out of a group of n objects is called

=

In latest notation system is also known as C(n;r) or

**Properties of **– It’s a very useful and interesting Mathematical tool. It has following properties.

(i) =

(ii)

(iii) known as Pascal’s law

(iv) r.

(v)

(vi) If n is even then we should put r=n/2 for maximum value of and if n is odd then is greatest when r=

(vii) In the expansions of if we put x=1 then