Combinations and Permutations Calculator

What are Combinations and Permutations?

Both combinations and permutations deal with counting and arranging items. The key difference is that:

• Permutations consider order as important.
• Combinations consider order as unimportant.

Formulas:

Permutations: Number of ways to arrange 'r' items out of 'n' items:

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

Combinations: Number of ways to choose 'r' items from 'n' items:

C(n, r) = n! / [r!(n-r)!]

How to Use the Calculator:

1. Select whether you want to calculate permutations or combinations.
2. Input the total number of items (n).
3. Input the number of items to arrange or choose (r).
4. Click on the "Calculate" button.
5. The calculator will give you the number of possible permutations or combinations.

Example:

Permutations:

How many ways can we arrange 3 books out of 5 on a shelf?

P(5, 3) = 5! / (5-3)! = 60 ways

Combinations:

How many ways can we choose 2 fruits out of 5?

C(5, 2) = 5! / [2!(5-2)!] = 10 ways

Applications:

• Game Strategies: Calculating possible moves in board games.
• Lottery: Determining the probability of winning based on combinations.
• Team Selection: Deciding how many ways players can be arranged or chosen for a match.