Please point me in the right direction. Thanks in advance

[stephencourtney]

Hey there guys,

I hope this is in the right section however in not apologies and feel free to move it.

I am trying to figure out all possible combinations of a number of selections and numbers, lets say for example a,b,c,d and 1,2,3.

The numbers are the variables spread across the letters for example the first few would be.

a -1, b -1, c -1, d -1
a -1, b -1, c -1, d -2
a -1, b -1, c -2, d -1
a -1, b -2, c -1, d -1
a -2, b -1, c -1, d -1

I have tried writing them down but it just gets very confusing, if any of you could point me to a calculator or an easier way of doing this I would really appreciate it.

Thanks a lot in advance for your help guys.

Stephen

 

[HallsofIvy]

If I understand this correctly, you need "the fundamental theorem of counting": if event A can happen in n ways and then event B can happen in m ways, the two events can happen together in mn ways (the product). Here there are 4 ways to get a letter and three ways to get a number so there are a total of (4)(3)= 12 ways to do this.

Hmmm, that doesn't fit what you show so I didn't understand! It seems that, instead you always have a, b, c, and d and each of those can have 1, 2, or 3. So there are 3 possible "an" terms(a1, a2, or a3), 3 possible "bn" terms, 3 possible "cn" terms, and 3 possible "dn" terms. That is a total of 3(3)(3)(3)= 81 possible ways.