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Solution


Q.

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is __________.          [2025]

Ans.

(1405)

(i) Single letter is used, then number of words = 5

(ii) Two distinct letters are used, then number of words

              =C25×(6!2!4!×2+6!3!3!)=10(30+20)=500

(iii) Three distinct letters are used, then number of words

             =C35×6!2!2!2!=900

∴   Total number of words = 1405.