A bowl of distinct wooden tokens and an empty selection tray. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Uniqueness changes the later draws
Drawing two values from the integers 1 through 5 without replacement produces distinct values. The first value is uniform across five choices. Once it is observed, the next value is uniform across the four remaining choices, so the two draws are dependent. A duplicate-free list is not a list of independent draws.
Compare one simple event
The chance of drawing 1 then 2 without replacement is (1/5)(1/4) = 1/20. With replacement, it is (1/5)(1/5) = 1/25. Drawing two copies of 1 is impossible without replacement but has probability 1/25 with replacement. The sampling mode changes both the available outcomes and their probabilities.
Specify whether list order matters
The Random Number Generator returns a random ordered list. When replacement is disabled, each remaining integer is equally likely at the next step. Sorting the list afterward can make it easier to read, but the sorted positions no longer represent the original draw order.
Keep sampling distinct from counting
The number of unordered size-two subsets from five is C(5,2) = 10, while the number of ordered no-replacement draws is 5×4 = 20. Use the Permutation Calculator for the latter count and Combination Calculator for the former. Read inclusive bounds to avoid a range-size error before generating the sample. The generator is an educational browser tool, not a seeded audit trail or a guarantee about the representativeness of a real-world sampling frame.
Check the model behind your result
Use the Random Number Generator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26