Question

With 10 different letters, 5 letter words are formed. Then the number of words which have atleast one letter repeated is

• A. ${10}^5$
• B. ${}^1{}^0{P}_5$
• C. ${10}^5-{}^1{}^0{P}_5$
• D. $5{}^1{}^0$

Answer 1

The correct option is C ${10}^5-{}^1{}^0{P}_5$

Total number of ways in which the 5 letter word can be formed with repetition allowed is ${10}^5$

The number of ways in which the 5 letter word can be formed where no digit is repeated is ${}^{10}{P}_5$

Thus the number of ways where at least one digit is repeated is

${10}^5{-}^{10}{P}_5$