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# Counting

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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?

Jan 28, 2022

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.