10 different letters of the English alphabet | vedclass

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Question

(A) The total number of words of $5$ letters that can be formed using $10$ different letters,where repetition is allowed,is $10^5 = 100000$.
The numb

Vedclass · Accepted Answer

$69760$

Vedclass · Answer

(A) The total number of words of $5$ letters that can be formed using $10$ different letters,where repetition is allowed,is $10^5 = 100000$.
The number of words of $5$ letters where all letters are distinct is given by the permutation formula $P(10, 5) = \frac{10!}{(10-5)!} = 10 	imes 9 	imes 8 	imes 7 	imes 6 = 30240$.
The number of words with at least one letter repeated is calculated as: (Total number of words) - (Number of words with all distinct letters).
Therefore,the required number of words is $100000 - 30240 = 69760$.

$10$ different letters of the English alphabet are given. Out of these letters,words of $5$ letters are formed. How many words can be formed if at least one letter is repeated?

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