Number of 6- letter words, with or without meaning, that can be formed using letters of word text{MA

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6.Permutation and Combination

hard

The number of $6-$letter words, with or without meaning, that can be formed using the letters of the word $\text{MATHS}$ such that any letter that appears in the word must appear at least twice, is $. . . .. .. $

A$1750$

B$1503$

C$1320$

D$1405$

(JEE MAIN-2025)

Solution

$(i)$ Single letter is used, then no. of words $=5$
$(ii)$ Two distinct letters are used, then no. of words
${ }^5 C_2 \times\left(\frac{6!}{2!4!} \times 2+\frac{6!}{3!3!}\right)=10(30+20)=500$
$(iii)$ Three distinct letters are used, then no. of words
${ }^5 C_3 \times \frac{6!}{2!2!2!}=900$
Total no. of words $=1405$

Standard 11

Mathematics

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medium

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hard

(JEE MAIN-2021)

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normal

The number of $6-$letter words, with or without meaning, that can be formed using the letters of the word $\text{MATHS}$ such that any letter that appears in the word must appear at least twice, is $. . . .. .. $

Solution

Similar Questions

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