Sorteios com Reposição
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
n^k
About this calculator
The Draws with Replacement calculator solves counting problems where, after each draw, the element is returned to the original set. This means the same item can be drawn more than once, and the order of draws matters. For example, drawing 3 numbered balls from 1 to 10 with replacement yields 10^3 = 1000 possible sequences.
The formula used is n^k, where n is the number of available elements and k is the number of draws. This expression comes from the fundamental counting principle: for each draw there are n possibilities, and since draws are independent, we multiply the possibilities for each step. The result is the total number of ordered sequences possible.
You can use this calculator in situations such as lottery draws with repeated numbers, choosing alphanumeric passwords (where characters can repeat), or any experiment where an element is drawn and replaced. It is common in basic probability and combinatorics problems.
Caution: do not confuse with combinations or arrangements without replacement. If draws are without replacement, the formula changes. Also, remember that order matters: swapping the sequence of draws yields a different result. Check if the problem truly allows repetition before using n^k.
Frequently asked questions
What does 'with replacement' mean in draws?
It means that after each draw, the drawn element is returned to the set, so it can be drawn again. This allows repetitions in the sequence.
What is the difference between draws with and without replacement?
With replacement, the same element can appear multiple times; without replacement, each element can only be drawn once. The formulas differ: n^k for with replacement and permutation/combination for without.
Can I use this calculator to compute probabilities?
Yes, the result n^k is the total number of possible outcomes. For the probability of a specific event, divide the number of favorable outcomes by n^k.
What if order does not matter?
If order does not matter, you need combinations with repetition, not n^k. This calculator considers the order of draws.
How to calculate if there are multiple sets of elements?
If each draw is from a different set (e.g., first from A, second from B), multiply the sizes: |A| * |B| * ... . The formula n^k assumes the same set for all draws.