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:
Ck′(n)=(kn+k−1) n=10 k=4 C4′(10)=C4(10+4−1)=C4(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:Ck′(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
- Chocolates
In the market, we have 3 kinds of chocolates. How many ways can we buy 8 chocolates?
- Candy
How many ways can 10 identical candies be divided among 5 children?
- Cinema
How many ways can 11 free tickets to the premiere of "Jáchyme throw it in the machine" be divided between 6 pensioners?
- Cards
How many ways can you give away 32 playing cards to 7 player?
- Hockey game
In the hockey game, they scored six goals. The Czechs played against Finland. The Czechs won 4:2. In what order did they fall goals? How many game sequences were possible during the game?
- Divide
How many different ways can three people divide seven pears and five apples?
- Four-digit 3912
Create all four-digit numbers from digits 1,2,3,4,5, which can repeat. How many are there?
- Represented 4324
A bag contains 20 candies in five different flavors: cherry, lemon, orange, mango, and cola. We know that there is at least one of each flavor in the pocket and that there are twice as many lemons as cherry ones. How many ways can different flavors be rep
- Salami
We have six kinds of salami, six of which have ten pieces, and one of which has four pieces. How many ways can we distinctly choose five pieces of salami?
- Alternate 4766
Each of the three players draws 3 top cards from the deck of 54 cards and returns one card to the deck from the bottom. The first, second, and third players alternate regularly. In which round does the first player draw again the card he got rid of in the
- Cards
From a set of 32 cards, we randomly pull out three cards. What is the probability that it will be seven kings and an ace?
- Roses 2
Aunt Rose went to the flower shop to buy three rose bouquets. The flower shop had white, yellow, and red roses. How many different flowers bouquets can a flower make for Aunt Rose create? Write all the bouquet options.
- Bouquets
The flower shop sells roses, tulips, and daffodils. How many different bouquets of five flowers can we make?
- Three reds
What is the probability that all three of the seven cards will be red if three cards are drawn?
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