Combination calculator

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A Combination is a concept where out of certain number of items, few are picked. If there are given number of items, and we have the option of choosing only a certain number from the given, then we use the Combination formula to calculate the possibilities. Combination calculator is an instant online tool helpful in finding the total number of combinations possible for a given set.


Example 1: In a bag there are 10 fruits and among them, there are 6 apples. How many different ways are there for a person to pick only the apples without looking inside the bag.


Combination formula  nCr =         n!
                                                   (n – r)! * r!

Given number of items, n = 10

Number of items to be chosen, r = 6

10! = 10* 9 * 8 * 7 * 6* 5 * 4 * 3 * 2 * 1

10C6 = 10! / [(10-6)! * 6!]

10C6 = 10! / (4! * 6!) = 210



Example 2: In a class, out of 5 students 3 can be picked for a competition. How many different ways are there to pick 3 students out of 5?


Combination formula  nCr =      n!
                                                (n – r)! * r!

Given number of items, n = 5

Number of items to be chosen, r = 3

5! = 5 * 4 * 3 * 2* 1

5C3= 5! / [(5 - 3)! * 3!]

10C6 = 5! / (2! * 3!) = 10


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