Tool to generate combinations with repetitions. In Mathematics, a combination with repetitions is a combinations of items which can be repeated.
Combinations with Repetition - dCode
Tag(s) : Mathematics
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Tool to generate combinations with repetitions. In Mathematics, a combination with repetitions is a combinations of items which can be repeated.
Item combinations with repetition consist in generating the list of all possible arrangements of elements (each can be repeated) in any order.
Example: A,B,C items be shuffled in 6 couples of 2 items: A,A A,B A,C B,B B,C, C,C. Without repetition, there would be only 3 couples A,B, A,C et B,C.
The sets of n elements are called tuples: {1,2} or {1,2,3} are tuples.
Counting repeated combinations of k items (sometimes called k-combination) in a list of N is noted \( \Gamma_n^k \) and $$ \Gamma_n^k = {n+k-1 \choose k} = \frac{(n+k-1)!}{k! (n-1)!} $$
The number of combinations with repeats of \( k \) items among \( N \) is equal to the number of combinations without repeats of \( k \) items among \( N + k - 1 \).
The calculation of the combinations generates an exponential number of values which require large calculation servers, generations have therefore a cost.
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