Question

How many ternary strings of length 2 n are there in which the zeroes appear only in odd-numbered positions?

Answer 1

In a string of length $2n$, there are exactly $n$ odd-numbered posiitons. In the remaning $n$ even-numbered positions, we want to choose from only two possible digits, either a 1 or a 2. This means there are $2^n$ such ternary strings.