Q. 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) $\begin{pmatrix}
8 \\
4
\end{pmatrix} - \ ^{8}P_{4}$
B) $8^{4} + \begin{pmatrix}
8 \\
4
\end{pmatrix}$
C) $8^{4} - \ ^{8}P_{4}$
D) $8^{4} - \begin{pmatrix}
8 \\
4
\end{pmatrix}$
Explanation
(c)
Total number of words formed by 4 letters form given eight different letters with repetition$= 8^{4}$
and number of words with no repetition$=^{8}P_{4}$
$\therefore$ Required number of words$= 8^{4} - {\ ^{8}P}_{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.