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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

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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

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  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




    Answer  :  

    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



    Answer  :  

    Permutations = 8910720 possible arrangements

     

     

     

    Combination = 12376 possible selections



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