Question

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

• A. ${}^8{C}_4{-}^8{P}_4$
• B. $8^4{+}^8{C}_4$
• C. $8^4{-}^8{P}_4$
• D. $8^4{-}^8{C}_4$

Answer 1

The correct option is C $8^4{-}^8{P}_4$

Total words =$8^4$ Total words without repetition =${}^8{P}_4$ Number of words with atleast one letter Repeated $=8^4{-}^8{P}_4$.