JEE MAIN - Mathematics (2025 - 29th January Morning Shift - No. 25)
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 _________.
Answer
1405
Explanation
(i) Single letter is used, then no. of words $=5$
(ii) Two distinct letters are used, then no. of words
$${ }^5 \mathrm{C}_2 \times\left(\frac{6!}{2!4!} \times 2+\frac{6!}{3!3!}\right)=10(30+20)=500$$
(iii) Three distinct letters are used, then no. of words
$${ }^5 \mathrm{C}_3 \times \frac{6!}{2!2!2!}=900$$
Total no. of words $=1405$
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