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

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(A) The total number of words of $5$ letters that can be formed using $10$ different letters (with repetition allowed) is $10^5 = 100000$.The number of words in which no letter is repeated is given by the permutation formula $^{10}P_5 = 10 \times 9 \times 8 \times 7 \times 6 = 30240$.The number of words with at least one letter repeated is equal to the total number of words minus the number of words with no letter repeated.Required number of words $= 100000 - 30240 = 69760$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. The number of words which have at least one letter repeated is

IIT 1980 All IIT

A
$69760$
B
$30240$
C
$99748$
D
None of these

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Permutations and Combinations

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. The number of words which have at least one letter repeated is

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