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
- Cinema
How many ways can 11 free tickets to the premiere of "Jáchyme throw it in the machine" be divided between 6 pensioners?
- Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
- Opportunities 8372
There are 20 students in the class, four of them are being tested by the teacher. How many options are there to choose who the teacher will test?
- Sons
The father has six sons and ten identical, indistinguishable balls. How many ways can he give the balls to his sons if everyone gets at least one?
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