How many combinations of 3 out of ten numbers?

Answer 1

There are 10 x 9 x 8 ways to select 3 numbers from 10 in order (permutations of 3 numbers from 10), but as want the number of combinations, the order doesn't matter, so need to divide by the number of ways 3 numbers can be ordered which is 3 x 2 x 1. Thus:

combinations(3 from 10) = (10 x 9 x 8)/(3 x 2 x 1)

= 120.

There are formulae for the number of permutations and combinations of r items chosen from a set of n items:

Permutations: nPr = n!/(n-r)!

Combinations: nCr = n!/(n-r)!r!

Where n! means "n factorial" which is the product of n with all numbers less than it to 1, ie n! = n x (n-1) x ... x 2 x 1

The combinations nCr is also written as a vector with n over r, as in (nr), but it is difficult to show the n exactly over the r as it should be (with the characters available) so I use the nCr format which is found on scientific calculators.