I am trying to figure out a formula for combinations of certain variations of a set

[jigsawe]

Hi

I am trying to figure out a formula for combinations of certain variations of a set

for example:

a combination of 5 with 3 variations each
a1, a2, a3
b1, b2, b3
c1, c2, c3
d1, d2, d3
e1, e2, e3

So a combination could be
a1 b1 c1 d1 e1
a2 b1 c1 d1 e1
a3 b1 c1 d1 e1
a1 b2 c1 d1 e1
a1 b3 c1 d1 e1 ... etc

and order would matter, so:

a1 b3 c1 d1 e1 would be the same as e1 d1 c1 b3 a1

is it as simple as 3^5=243 ?

Hope im making sense, any help would be appreciated!

 

[Dr.Peterson]

Hi

I am trying to figure out a formula for combinations of certain variations of a set

for example:

a combination of 5 with 3 variations each
a1, a2, a3
b1, b2, b3
c1, c2, c3
d1, d2, d3
e1, e2, e3

So a combination could be
a1 b1 c1 d1 e1
a2 b1 c1 d1 e1
a3 b1 c1 d1 e1
a1 b2 c1 d1 e1
a1 b3 c1 d1 e1 ... etc

and order would matter, so:

a1 b3 c1 d1 e1 would be the same as e1 d1 c1 b3 a1

is it as simple as 3^5=243 ?

If I'm understanding you correctly, yes.

It appears that a "combination" here means choosing one of the three variations of each of 5 items. There are 3 ways to choose an "a", and for each of those there are 3 ways to choose a "b", and so on, for a total of 3^5 ways.