Math CentralQuandaries & Queries


Question from ivana, a student:


How many possible 3-digit combinations can be made of the numbers 123456?
None of the numbers can repeat in one combination. I used to know a formula but have been out of school for some time and cannot remember.

Thank you.


If order is not important, for example 135 is the same as 351, then you want the number of ways of choosing 3 things from 6 things. This is called "6 choose 3" and it is written

\[\left( \begin{array}{c}6\\3 \end{array} \right) = \frac{6!}{3! (6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20.\]

If order is important then these are called permutations. You have 6 choices for the first digit, 5 choices for the second digit and 4 choices for the third digit so you have

\[6 \times 5 \times 4 = 120 \mbox{ permutations.}\]


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS