How many strings of length 5 of the letters A, B, C, D, and E contain exactly one A and exactly one D if repetition of letters is allowed?
+2668 There is 5 options of where to put the A. There is 4 options of where to put the D, because the A takes up one spot. FOr the remaining 3 slots, there is \(3^3 = 27 \) ways to arange them, so the answer is \(27 \times 20 = \color{red}540 \) ways.
