# How To Solve Permutations And Combinations Problems

Tutorial on permutation and combination definition, formula and solved problems.

## Permutation Formula With Example

**Permutation** is a set of "**Ordered Combination**". **Combination** refers to set of things **without considering the order**. If the order matters on arranging a set of certain object or things, then its called as permutation. When the order doesnt matter in the arrangement then its known as combination. Learn here how to solve permutations and combinations problems with detailed explanation.

**Easy Permutation and Combination Example:**

Lets have a clarity about these terms with an example.

I had a smoothie blended with the blueberries, vanilla extract, peeled banana, raspberries and orange juice. Here you dont need to bother about the order of the ingredients. Because whatever order we make up, it will be the same smoothie. This is what we refer as **Combination**.

Class A has 45 brilliant students, class B is filled with 70 average students and Class C is occupied by 50 dull students. Here you cannot exchange the strength of the classes. This is **permutation**.

**Permutation Formula:**

Given here the permutation formula with example for solving the statistical permutation.

P(n,r)=n! / (nâˆ’r)!

"!" - Symbol of Factorial

n - number of permutations

**Permutation Example:**

**Step 1:** There are six members selected for five different positions: director, president, vice president, general secretary and CEO. CEO will be chosen first followed by the other four positions. What are the possible ways for filling these positions?

n=6

r=5

**Step 2:** First thing is to figure out is whether the problem is about solving **permutation or combinations.** Here you should consider the order of appointment of people for different positions. So its a permutation problem.

**Step 3: **Substitute the values in the formula.

Only five positions are available for the six members. Therefore, total number of ways (n) you can choose from is 6 and number of available position(r) is 5.

P(n,r)=n! / (nâˆ’r)!

P(n,r)= 6! / (6-5)!

=6 x 5 x 4 x 3 x 2 x 1 / 1!

=6 x 5 x 4 x 3 x 2 x 1 / 1

=720

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