# How to Calculate The Probability of Combination

Tutorial on how to solve combination problems with examples.

## Combination Formula

When order doesnt matter in arranging things, then its called as combination. Lets learn how to calculate the probability of combination problem with example using formula given below.

**C(n,r)= ****n! / r!(nâˆ’r)!**

"!" - Symbol of Factorial

n - number of combinations

**Steps To Follow**

**Step 1:** Consider picking 3 people randomly from the group of 8 for playing an outdoor game. Find the possible number of combinations.

**Step 2:** Here you can choose people in any order, thus its a combination problem.

Substitute the given values in the combination formula.

n = 8

r = 3

C(n,r)= n! / r!(nâˆ’r)!

C(8, 3) = 8! / 3!(8-3)!

= 8! / 3!(5)!

=8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 3 x 2 x 1 (5 x 4 x 3 x 2 x 1)

=40320/6 (120)

=40320/ 720

=56

The possible combinations are 56.

## Related Topics