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Q.

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

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a

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

b

$8^{4} + (\begin{matrix} 8 \\ 4 \end{matrix})$

c

$8^{4} - (\begin{matrix} 8 \\ 4 \end{matrix})$

d

$(\begin{matrix} 8 \\ 4 \end{matrix}) -^{8} P_{4}$

answer is C.

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Detailed Solution

Number of words with at least one letter repeated

$= n^{r} -^{n} P_{r}$

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

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