Question

Ten different letters 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. $69,760$
• B. $30,240$
• C. $99,748$
• D. None of these

Answer 1

The correct option is A $69,760$

The number of words in which all the 5 letters are repeated $={10}^5=100000$ and the number of words in which no letter is repeated $={{}^{10}P}_5=\frac{10!}{5!}=30240$

So the required umber of ways $=100000-30240=69760$