# Combinations and Permutations Calculator

## Calculate combinations and permutations step by step

The calculator will find the number of permutations/combinations, with/without repetitions, given the total number of objects and the number of objects to choose. It will also generate the list of r-combinations (r-permutations) from the given list, with steps shown.

Optional and can be comma-separated.

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Find the number of permutations with repetitions $\tilde{P}{\left(11,6 \right)}$.

Generate the list of 6-permutations with repetitions of {B, A, N, A, N, A}.

### Solution

The formula is $\tilde{P}{\left(n,r \right)} = n^{r}$.

We have that $n = 11$ and $r = 6$.

Thus, $\tilde{P}{\left(11,6 \right)} = 11^{6} = 1771561$.

Now, deal with the list.

Count the number of occurrences of each element: B occurs 1 time, A occurs 3 times, N occurs 2 times.

Thus, the number of elements in the generated list is $N = \frac{6!}{1! 3! 2!} = 60$ (for calculating the factorial, see factorial calculator).

$\tilde{P}{\left(11,6 \right)} = 1771561$
The number of elements in the generated list is $60$A.