Math CentralQuandaries & Queries

Question from Sarah:

Hello! My question is:
If I have 5 columns of numbers, and I want to create all possible combinations
(or is it permutations?) How can I do that? For example all numbers in each
column may not appear in any other column. so:
column 1: 1,2,3,4,5
column 2: 6,7,8,9,10
column 3: 11,12,13,14,15
column 4: 16,17,18,19,20
column 5: 21,22,23,24,25

how may I determine all the possible ways I can get sets of 5 out if this? Thanks!


Hi Sarah,

As I read this you are to choose one number from each column to get a set of 5 numbers.

If this is correct then there are 5 ways to choose a number from the first column and regardless of which number you choose you have 5 ways to choose a number from the second column. Hence there are $5 \times 5 = 5^2$ ways to create a set of 2 numbers, one from each of the first two columns.

For each of these $5^2$ ways to choose a 2 number set there are 5 ways to choose a number from the third column and hence there are $5^2 \times 5 = 5^3$ ways to choose a 3 number set from the first three columns.

I hope this helps. let me know if I have misinterpreted your question.


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