Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of…

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 :
  1. $\left(\begin{array}{l}8 \\ 4\end{array}\right)-{ }^8 P_4$
  2. $8^4+\left(\begin{array}{l}8 \\ 4\end{array}\right)$
  3. $8^4-{ }^8 P_4$
  4. $8^4-\left(\begin{array}{l}8 \\ 4\end{array}\right)$

Solution

Total number of words formed by 4 letters given from eight different letters with repetition $=8^4$ and number of words with no repetition $={ }^8 P_4$ $\therefore \quad$ Required number of words $=8^4-{ }^8 P_4$

Asked in: AP EAMCET 2006

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