PERMUTATIONA
Returns the number of permutations of k items from n with repetitions allowed: n^k.
PERMUTATIONA(number, number_chosen)Arguments
numberThe total number of items (must be ≥ 0).number_chosenThe number of items chosen (must be ≥ 0).
=PERMUTATIONA(3,2)3² = 9 ordered arrangements with repetition
=PERMUTATIONA(10,4)10⁴ = 10000 (e.g. 4-digit PIN combinations)
- •Available since Excel 2013
- •Returns #NUM! if either argument is negative
- •Use PERMUT() if items cannot repeat, COMBIN() if order does not matter
- •Confusing PERMUTATIONA with PERMUT - PERMUTATIONA allows items to repeat (like digits in a PIN code), while PERMUT assumes each item can only be used once, and the two produce very different results for the same inputs
- •Expecting the result to grow linearly - since PERMUTATIONA calculates n raised to the power of k, results grow exponentially and can become enormous very quickly as number_chosen increases
- •Passing a negative number to either argument, which returns a #NUM! error since permutations with repetition are only defined for non-negative counts
PERMUTCounts permutations without repetition, the more restrictive scenario that PERMUTATIONA generalizes by allowing items to be reused.COMBINACounts combinations with repetition where order doesn't matter, a related but distinct scenario from PERMUTATIONA's order-sensitive, repetition-allowed counting.POWERDirectly calculates the same n^k result that PERMUTATIONA computes, since the formulas are mathematically identical.What's the difference between PERMUTATIONA and PERMUT?
PERMUTATIONA allows the same item to be selected multiple times (like repeated digits in a PIN), while PERMUT assumes each item can only be chosen once. They represent genuinely different counting scenarios and give different results.
Why does PERMUTATIONA's result grow so fast?
It's calculated as number raised to the power of number_chosen, so results grow exponentially - even modest inputs like PERMUTATIONA(10,6) produce a million.
When would I use PERMUTATIONA in practice?
It's commonly used for counting things like possible passwords or PIN codes, where the same character or digit is allowed to appear more than once and the order matters.
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