Question

Ten different letters of English alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

• A. $30240$
• B. $69760$
• C. $99748$
• D. None of the above

Answer 1

The correct option is B $69760$

Number of words with no restriction $=(10{)}^5=100000$
and the number of words in which no letter is repeated $=10\cdot 9\cdot 8\cdot 7\cdot 6=30240$

Thus, the number of words which have at least one repeated letter $=100000-30240=69760$