# Combinations with repetition

The calculator finds the number of combinations of the k-th class from n elements with repetition. A combination with repetition of k objects from n is a way of selecting k objects from a list of n. The order of selection does not matter and each object can be selected more than once (repeated).## Calculation:

$C_{k}(n)=(kn+k−1 )n=10k=4C_{4}(10)=C_{4}(10+4−1)=C_{4}(13)=(413 )=4!(13−4)!13! =4⋅3⋅2⋅113⋅12⋅11⋅10 =715$

### The number of combinations with repetition: 715

# A bit of theory - the foundation of combinatorics

## Combinations with repeat

Here we select k element groups from n elements, regardless of the order, and the elements can be repeated. k is logically greater than n (otherwise, we would get ordinary combinations). Their count is:$C_{k}(n)=(kn+k−1 )=k!(n−1)!(n+k−1)! $

Explanation of the formula - the number of combinations with repetition is equal to the number of locations of n − 1 separators on n-1 + k places. A typical example is: we go to the store to buy 6 chocolates. They offer only 3 species. How many options do we have? k = 6, n = 3.

## Foundation of combinatorics in word problems

- Contestants 67104

The contestants have to create an ice cream sundae containing three different types of ice cream. They can use cocoa, yogurt, vanilla, hazelnut, punch, lemon and blueberry ice cream. How many different ice cream sundaes can the contestants create? - Kenneth 2

Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents? - Five-digit numbers

How many different five-digit numbers can be created from the number 2,3,5 if the number 2 appears in the number twice and the number 5 also twice? - Six attractions

How many opportunities do you have if you want to complete ten rides on the fair, but there are only six attractions? - The gems

The jeweler selects four gems for the ring. It has rubies, emeralds, and sapphires. How many options does he have?

more math problems »