Question

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 :

• A. $\left(\begin{array}{l}8 \\ 4\end{array}\right)-{ }^{8} P_{4}$
• B. $8^{4}+\left(\begin{array}{l}8 \\ 4\end{array}\right)$
• C. $8^{4}-{ }^{8} P_{4}$
• D. $8^{4}-\left(\begin{array}{l}8 \\ 4\end{array}\right)$

Answer 1

Answer: (C)

Total number of words formed by $4$ letters given from eight different letters with repetition $=8^{4}$ and number of words with no repetition $={ }^{8} P_{4}$
$\therefore $ Required number of words $=8^{4}-{ }^{8} P_{4}$