Question

Ten different letters of an alphabet are given words with five letters are formed from these given letters. Then, the number of words which have atleast one letter repeated, is

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

Answer 1

The correct option is A $69760$

The total number of $5$ letters words which can be formed atleast one or more of its letter is repeated
$=10\times 10\times 10\times 10\times 10={10}^5$

The number of $5$ letter words which can be formed when none of letter is repeated
$={{}^{10}P}_5=30240$

Therefore, the number of 5 letter words which have atleast one of their letters repeated
$100000-30240=69760$