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.
(iii) known as Pascal’s law
(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