Question

Ten different letters of English alphabet are given. Out of these letters, words of $5$ letters are formed. How many words are formed when at least one letter is repeated?

• A. $69760$
• B. $98748$
• C. $96747$
• D. $97147$

Answer 1

The correct option is A

$69760$

Explanation for the correct answer:

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

$=69760$

Therefore, the correct answer is option (A)