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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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Your Input

Find the number of permutations with repetitions P~(11,6)\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 P~(n,r)=nr\tilde{P}{\left(n,r \right)} = n^{r}.

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

Thus, P~(11,6)=116=1771561\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=6!1!3!2!=60N = \frac{6!}{1! 3! 2!} = 60 (for calculating the factorial, see factorial calculator).

Answer

P~(11,6)=1771561\tilde{P}{\left(11,6 \right)} = 1771561

The number of elements in the generated list is 6060A.

The generated list is {A, A, A, B, N, N}, {A, A, A, N, B, N}, {A, A, A, N, N, B}, {A, A, B, A, N, N}, {A, A, B, N, A, N}, {A, A, B, N, N, A}, {A, A, N, A, B, N}, {A, A, N, A, N, B}, {A, A, N, B, A, N}, {A, A, N, B, N, A}, {A, A, N, N, A, B}, {A, A, N, N, B, A}, {A, B, A, A, N, N}, {A, B, A, N, A, N}, {A, B, A, N, N, A}, {A, B, N, A, A, N}, {A, B, N, A, N, A}, {A, B, N, N, A, A}, {A, N, A, A, B, N}, {A, N, A, A, N, B}, {A, N, A, B, A, N}, {A, N, A, B, N, A}, {A, N, A, N, A, B}, {A, N, A, N, B, A}, {A, N, B, A, A, N}, {A, N, B, A, N, A}, {A, N, B, N, A, A}, {A, N, N, A, A, B}, {A, N, N, A, B, A}, {A, N, N, B, A, A}, {B, A, A, A, N, N}, {B, A, A, N, A, N}, {B, A, A, N, N, A}, {B, A, N, A, A, N}, {B, A, N, A, N, A}, {B, A, N, N, A, A}, {B, N, A, A, A, N}, {B, N, A, A, N, A}, {B, N, A, N, A, A}, {B, N, N, A, A, A}, {N, A, A, A, B, N}, {N, A, A, A, N, B}, {N, A, A, B, A, N}, {N, A, A, B, N, A}, {N, A, A, N, A, B}, {N, A, A, N, B, A}, {N, A, B, A, A, N}, {N, A, B, A, N, A}, {N, A, B, N, A, A}, {N, A, N, A, A, B}, {N, A, N, A, B, A}, {N, A, N, B, A, A}, {N, B, A, A, A, N}, {N, B, A, A, N, A}, {N, B, A, N, A, A}, {N, B, N, A, A, A}, {N, N, A, A, A, B}, {N, N, A, A, B, A}, {N, N, A, B, A, A}, {N, N, B, A, A, A}.