Hi there i am trying to work out the total possible number of combinations for a music system i have created. The system has 4 different instruments with each instruments having a varying number of variations.
Instrument 1 = 2 variations. Instrument 2 = 3 variations. Instrument 3 = 2 variations. instrument 4 = 3 variations.
The only way i could think to do this is times them all together resulting in 36 is this correct?
Correct! When you have independent events $e_1, e_2, ..., e_n$ and $N(e_k)$ gives the number of options for event $e_k$, the total number of combinations for events $e_1$ through $e_n$ is given by $$\prod_{k=1}^n N(e_k)$$
In other words, yes, you just multiply them together.
Yes.
In general, if process $1$ can be done in $m$ ways, and process $2$ can be done in $n$ ways, then the number of ways to do both processes is $m\times n$. This formula extends to any finite number of processes, so in this case, you just calculate: $$2\times 3\times 2\times 3=36,$$
as you did.
