Question

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

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

Answer 1

The correct option is A

$69760$

Explanation for the correct answer:

Counting of numbers:

Given ten different letters of alphabets.

Number of words of letters $5$ formed by repeating all these $10$ letters $={10}^5$

$=100000$

Number of words of letters $5$ formed by not repeating any of these $10$ letters $=10\times 9\times 8\times 7\times 6$

$=30240$

Hence, number of words of letters $5$ formed by repeating atleast one of the $10$ letters $=100000-30240$

$=69760$

Therefore, the correct answer is option (A).