counting combinations of 3 letters

Question

I have 3 arrays of letters: A, B, C

A is of length $3$ ($A_0$ to $A_2$)

B can be B$_0$ - B$_7$

C can be C$_0$ - C$_5$

Can I calculate the total number of all unique $3$ letter long combinations, without programatically permuting through them?

A0 B0 C0
A0 B0 C1
A0 B0 C2
A0 B0 C3
A0 B0 C4
A0 B0 C5
A0 B1 C0
A0 B1 C1
...

Answer 1

Well like @JMoravitz said, you have $3$ options for the first blank, $8$ options for the second one and $6$ for your third blank. So you get, $6\times8\times3$ = $144$. $$ $$ Normally for questions about combinations related to letters where the letters are the same you remove some combinations as the order doesn't matter but in this case, you have $A_0$ to $A_2$ so these two letters despite being the same have a small difference being their number. So you just calculate the permutations.