The number of possible combinations of 3 numbers depends on the total number of numbers to choose from (denoted as nnn) and whether order matters or not.
- If order does not matter (combinations), the number of ways to choose 3 numbers out of nnn is given by the binomial coefficient formula:
(n3)=n!3!(n−3)!\binom{n}{3}=\frac{n!}{3!(n-3)!}(3n)=3!(n−3)!n!
This counts all unique groups of 3 numbers without regard to order.
- If order does matter (permutations), then the number of ways to choose and arrange 3 numbers from nnn is:
P(n,3)=n!(n−3)!P(n,3)=\frac{n!}{(n-3)!}P(n,3)=(n−3)!n!
For example, if choosing 3 numbers from digits 0 to 9 (10 numbers):
- Combinations: (103)=120\binom{10}{3}=120(310)=120
- Permutations: 10×9×8=72010\times 9\times 8=72010×9×8=720
The formula and values vary depending on the set size nnn and whether repetition is allowed or order matters.
