Verified Solution • 2025–26 Session moderate

QJEEM25Ma1039: JEE Main 2025 Mathematics - Class 11 JEEM25Ma1039 Solution: The number of 6-letter words, with or without meaning, that can …

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 _________.

Step-by-Step Verified Solution

(i) Single letter is used, then no. of words =5=5

(ii) Two distinct letters are used, then no. of words

5C2×(6!2!4!×2+6!3!3!)=10(30+20)=500{ }^5 \mathrm{C}_2 \times\left(\frac{6!}{2!4!} \times 2+\frac{6!}{3!3!}\right)=10(30+20)=500

(iii) Three distinct letters are used, then no. of words

5C3×6!2!2!2!=900{ }^5 \mathrm{C}_3 \times \frac{6!}{2!2!2!}=900

Total no. of words =1405=1405

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