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Permutations and Combinations Calculator
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 Permutations and Combinations Calculator is a online tool used to calculate permutation and combination.Permutation is a process of arranging 'n' objects taken 'r' at a time. Combination is a process of selecting 'n' objects taken 'r' at a time.

## Step by Step Calculation

Step 1 :

Permutations and Combinations Formula's

Permutation formula: P(n, r) = $\frac{(n!)}{((n-r)!)}$

Combination formula: C(n, r) = $\frac{(n!)}{(r!(n-r)!)}$ ,

where, n gives number of things, and r gives number of times.

Step 2 :

Put the values in the above formula's and solve it further.

## Example Problems

1. ### Calculate the number of permutations and combinations; n = 12, r = 4.

Step 1 :

Given: Here, n = 12, r = 4.

Permutation formula: P(n, r) = $\frac{(n!)}{((n-r)!)}$

Combination formula: C(n, r) = $\frac{(n!)}{(r!(n-r)!)}$ ,

where, n gives number of things, and r gives number of times.

Step 2 :

Put the values in the above formula's and solve it further.

Permutation formula: P(n, r) = $\frac{(n!)}{((n-r)!)}$

P(12, 4) = $\frac{(12!)}{((12 - 4)!)}$ = $\frac{(12 \times 11 \times 10 \times 9 \times 8!)}{(8!)}$

= 11880 possible arrangements

Combination formula: C(n, r) = $\frac{(n!)}{(r!(n-r)!)}$

C(12, 4) = $\frac{(12!)}{(4!(12 - 4)!)}$ = $\frac{(12 \times 11 \times 10 \times 9)}{(4 \times 3 \times 2 \times 1)}$

= 495 possible selections

Permutations = 11880 possible arrangements

Combination = 495 possible selections

2. ### Calculate the number of permutations and combinations; n = 17, r = 6.

Step 1 :

Given: Here, n = 17, r = 6.

Permutation formula: P(n, r) = $\frac{(n!)}{((n-r)!)}$

Combination formula: C(n, r) = $\frac{(n!)}{(r!(n-r)!)}$ ,

where, n gives number of things, and r gives number of times.

Step 2 :

Put the values in the above formula's and solve it further.

Permutation formula: P(n, r) = $\frac{(n!)}{((n-r)!)}$

P(17, 6) = $\frac{(17!)}{((17 - 6)!)}$ = $\frac{(17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11!)}{(11!)}$

= 8910720 possible arrangements

Combination formula: C(n, r) = $\frac{(n!)}{(r!(n-r)!)}$

C(17, 6) = $\frac{(17!)}{(6!(17 - 6)!)}$ = $\frac{(17 \times 16 \times 15 \times 14 \times 13 \times 12)}{(6 \times 5 \times 4 \times 3 \times 2 \times 1)}$

= 12376 possible selections

Permutations = 8910720 possible arrangements

Combination = 12376 possible selections

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