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Question

(C) The total number of words of length $4$ that can be formed using $8$ different letters with repetition allowed is $8 	imes 8 	imes 8 	imes 8 =

Vedclass · Accepted Answer

$8^{4} - {}^{8}P_{4}$

Vedclass · Answer

(C) The total number of words of length $4$ that can be formed using $8$ different letters with repetition allowed is $8 	imes 8 	imes 8 	imes 8 = 8^{4}$.The number of words of length $4$ that can be formed using $8$ different letters without any repetition is given by the permutation formula ${}^{n}P_{r} = {}^{8}P_{4}$.The number of words with at least one letter repeated is the total number of words minus the number of words with no letters repeated.Therefore,the required number of words is $8^{4} - {}^{8}P_{4}$.

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is :

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