20 things taken 8 at a time

HOME

Math Central

Quandaries & Queries

Question from Jessie, a student:

I need all of the 8 digit combinations using the numbers 1-20.
i.e. 1 2 3 4 5 6 7 8, 2 3 4 5 6 7 8 9 like wise
no number should be repeated in one combination.
Thanks
Jessie

Hi Jessie,

The number of such arrangements depends on whether order is important. If order is not important so that 12345678, 21345678, 87654321 and so on are the same arrangement then mathematicians call them combinations of 20 things taken 8 at a time. If order is important so that 12345678, 21345678, and 87654321 are all different then mathematicians call them permutations of 20 things taken 8 at a time.

You can calculate the number of combinations of 20 things taken 8 at a time and the number of permutations of 20 things taken 8 at a time on the Stat Trek web site. I got the number of combinations of 20 things taken 8 at a time to be 125,970 and the the number of permutations of 20 things taken 8 at a time to be 5,079,110,400. In either case too many to list.

Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.