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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

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

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.

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.