Question

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

• A. $69760$
• B. $30240$
• C. $99748$
• D. $42386$

Answer 1

Answer: (A)

$69760$

$10$ letters $5$ to be selected

Total number of $5$ letter words $={10}^5$

Number of words without repetition $={}^{10}{P}_5$

Number of words without at least one letter repeated

$=100000-(10\times 9\times 8\times 7\times 6)=69760$

Hence the correct answer is $69760$