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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 4 ____.

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answer is 1405.

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Detailed Solution

(i) Single letter is used, then no. of words = 5
(ii) Two distinct letters are used, then no. of words
 5C2×6!2!4!×2+6!3!3!=10(30+20)=500
(iii) Three distinct letters are used, then no. of words
 5C3×6!2!2!2!=900
Total no. of words = 1405

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