Correct answer option (A) 69760
Suppose we have 5 places, each of which is to be filled by one letter from the 10 letters. The first place may be filled in 10 ways. When repetitions of the letters are allowed, the second place may also be filled in 10 ways.
Proceeding in this way, it is clear that words with five letters are formed in 105 ways. These 105 ways also include the number of ways of forming words with all different letters without repetition. These are 10P5 in number. Therefore, the number of words which have at least one letter repeated is
105 – 10P5 = 100000 – 30240 = 69760
