The number of 6-letter words, with or without | vedclass

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Question

$(i)$ Single letter is used, then no. of words $=5$
$(ii)$ Two distinct letters are used, then no. of words
${ }^5 C_2 	imes\left(\frac{6!}{2!4!} \

Vedclass · Accepted Answer

$1405$

Vedclass · Answer

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

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 $. . . .. .. $

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