There are 10 distinct letters of the English | vedclass

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Question

(A) The total number of $5$-letter words that can be formed using $10$ distinct letters (with repetition allowed) is $10^5 = 100000$.The number of $5$

Vedclass · Accepted Answer

$69760$

Vedclass · Answer

(A) The total number of $5$-letter words that can be formed using $10$ distinct letters (with repetition allowed) is $10^5 = 100000$.The number of $5$-letter words that can be formed using $10$ distinct letters without any repetition is given by the permutation formula $^{10}P_5 = \frac{10!}{(10-5)!} = 10 	imes 9 	imes 8 	imes 7 	imes 6 = 30240$.The number of words with at least one letter repeated is the total number of words minus the number of words with no repeated letters.Required number of words = $100000 - 30240 = 69760$.

There are $10$ distinct letters of the English alphabet. Words of $5$ letters are formed using these letters. How many such words can be formed if at least one letter is repeated?

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