According to combinations definition, combination gives the possibility of occurrence of some thing where order is not a matter of concern. It gives the generalized possibility of a event to occur. Many logical problems can be solved using combinations. Now that we have learned what is combination, let us study combinations formula in detail and go forward with examples.

## A brief on combinations formula:

The formula for possible outcomes of 'r' things from a huge set of 'n' things is given by nCr, i.e. r possible outcomes of n. Here nCr = n! / (n – r)!r! where r and n are positive integers while ! Is the operator for factorial. It should be known that the factorial of a number is obtained by taking product of all non-negative integers less than the number. Here r is called the binomial coefficient. As said above, the order of occurrence is irrelevant in combination unlike permutation where order is of prime importance. By now, you must be familiar with combination definition and the formula. So lets move on to combination examples.

## Solving combination examples:

The combinations examples given below are meant to provide the real-life applications of combination. Combination can be applied to many logical problems. Lets see some of them.

(i) Find the combination 5C3:

Comparing with the formula, n = 5 and r = 3. Hence combination is given by 5C3 = 5! / (5-3)!3!

5C3 = 5! / 2!3! = 5 x 4 x 3! / (2 x 3!) = 10. Thus the answer is 10.

(ii) A class consists of 10 students. Find the number of ways 2 students can be selected out of it:

Here n = 10 while r = 2. Hence number of ways 2 students can be selected out of 10 is given by 10C2 i.e. 10! / (10-2)!2! = 10 x 9 x 8! / 8!2! = 45. Thus 2 students can be selected out of 10 in 45 different ways.

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