The word VENEZUELA consists of the letters V, E, N, E, Z, U, E, L, A. There are three E's in the word.

To select four letters containing exactly one E, we first choose one E. This leaves us with six other letters: V, N, Z, U, L, A.

We need to choose three more letters from these six. The number of ways to choose 3 letters from 6 is given by the combination formula:

\(\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20\)

Thus, the number of possible selections containing exactly one E is 20.