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!(n−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!(n−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.

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