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N choose K Calculator
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Let us assume that you have n no of toys and you are supposed to choose k no of toys. Here n choose k tells you that in how many ways we can choose k toys in the given n no of toys.
In the same way n choose k Calculator finds the combination of choosing k items in n no of items.
where n = total no of items
                                     k = no of items chosen.
 

Steps for N choose K Calculator

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Step 1 :  

Read the problem and find given no of items and how many items to be choosen.



Step 2 :  
Use the combination formula:

nck = $\frac{n!}{r!(n-k)!}$

where n = total no of items

k = no of items choosen.

Substitute the values in the formula to get the no of combinations.


Problems on N choose K Calculator

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  1. A dance show is going on and 15 children participating in that. In how many ways can a group of children be arranged such that 5 children accomodate each group?


    Step 1 :  

    Given: n = 15,
               k = 5



    Step 2 :  
    Use the combination formula:

    nck = $\frac{n!}{r!(n-k)!}$


           = $\frac{15!}{5!(15 - 5)!}$

         = $\frac{15 \times 14 \times 13 \times 12 \times 11 \times 10}{5! 10 !}$

         = $\frac { 15 \times 14 \times 13 \times 12 \times 11}{5!}$

         =  3003.



    Answer  :  

    There are 3003 ways of arranging a group such that 5 children accomodate each group. 



  2. In a lucky draw, 6 boxes are kept in which only 3 boxes contains gifts. In how many ways can the kids pick the gift boxes?


    Step 1 :  

    given: n = 6,


               k = 3 



    Step 2 :  

    Use the combination formula:


    nck = $\frac{n!}{r! (n-k)!}$


          = $\frac{6!}{3! (6 - 3)!}$


          = $\frac{6!}{3! 3!}$


          = $\frac{6 \times 5 \times 4 \times 3!}{3! 3!}$


          = $\frac{120}{36}$


          = 20 ways.



    Answer  :  

    There are 20 ways to select the gift boxes.



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