NCr Calculator

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Probability, ‘nCr’ is a formula used to express the number of combinations possible while choosing from a

given number of items. ‘n’ stands for the number of items and ‘r’ stands for the number of items we have to

pick. ‘nCr’ is the number of possible ways of choosing ‘r’ items from ‘n’ items. nCr calculator is the online tool

which can calculate ‘nCr’ value.

Example 1: Calculate the value of nCr if n = 6 and r = 2.

Given n = 6 and r= 2

According to the nCr formula -> nCr = n!/[r! *(n– r)!]

Applying the above formula, we get -> nCr = 6!/ [(4!* (4- 2)!]

6C4 = 6!/ (4!* 2!)

6! = 6 * 5 * 4 * 3 * 2 * 1

Similarly  2! = 2 * 1 and -> 4! = 4 * 3 * 2 * 1

Cancelling the common factors, we get

6C4 = 15

Example 2: In bag there are 5 candies, and out of them 3 should be picked. In how many possible

ways can we pick 3 candies?

Given n = 5 and r= 3

According to the nCr formula-> nCr = n!/[r! *(n– r)!]

Applying the above formula, we get-> nCr = 5!/ [(3!* (5 - 3)!]

5C3 = 5!/ (3!* 2!)

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

Similarly 2! = 2* 1 and-> 3! =3* 2* 1

Cancelling the common factors, we get-> 5C3 = 10

Hence there are 10 ways of picking 3 out of 5 candies.