The letters of the word MUMMY are placed at random in a row. What is the chance that letters at both the extremes are M?

The word MUMMY contains 5 letters with M repeated 3 times, so the total number of distinct arrangements is 5! / 3!, which equals 20. For the letters at both extremes to be M, we fix M at the first and last positions, leaving one M, one U, and one Y to arrange in the 3 middle positions. The number of arrangements for these 3 middle letters is 3!, which is 6. The probability is therefore 6/20, which simplifies to 1/5.

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