   SEARCH HOME Math Central Quandaries & Queries  Question from Errol: show me a list with all four digit combination numbers from 0 -9 Hi Errol,

Since you used the word combination I am going to assume that order is not important. For example 1234, 1324, 4213 etc. are all the same combination. If this is true then you are looking for all the ways of choosing 4 items from the 10 items, 0, 1, 2, ..., 9. There are 210 ways of choosing 4 items from 10. You can create a list of the 210 combinations using the Combinatorial Object Server at the University of Victoria in Victoria BC, Canada.

Follow the Subsets or Combinations link and then select the Combinations in lex order option. Enter $n = 10$ and $k = 4$ and then generate the combinations. A table with 210 rows is returned where each row is a sequence of 10 zeros and ones. Think of the table this way. I put a number at the top of each column and then duplicated the first three rows of the table.

1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 1 1 1 1
0 0 0 0 0 1 0 1 1 1
0 0 0 0 0 1 1 0 1 1
. . . . . . . . . .

Each row in the table represents a combination of 4 items from 0, 1, 2, ..., 9. A 1 in the any column indicates that the number at the top of that column is in the combination and a 0 in any column indicates that the number at the top of that column is not in the combination. Thus the first three rows represent the combinations 7, 8, 9, 10; 6, 8, 9, 10; and 6, 7, 9, 10.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.