jmc

Question

How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once? (Here, a word is an arbitrary sequence of letters.)

Accepted Answer

There are 4^3 three letter words from A, B, C, and D, and there are 3^3 three letter words from just B, C, and D. There must, then, be 4^3 - 3^3=64-27 = 37 words from A, B, C, and D containing at least one A.