If $\displaystyle A $ is a finite set, let $\displaystyle o(A) $ be its cardinality. Let $\displaystyle A $ be the set consisting of all $\displaystyle 5 $-digit integers, each digit of which is $\displaystyle 1,2 $ or $\displaystyle 3 $. Compute $\displaystyle o(A) $. Let $\displaystyle B = \{x \in A: \ \text{each of} \ 1,2, \ \text{and} \ 3 \ \text{is among the digits of} \ x \} $. Compute $\displaystyle o(B) $.

So $\displaystyle o(A) = 3^5 $? And $\displaystyle o(B) = 6 \times 10^2 = 600 $?