Question

7 different letters of the English alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:

• A. 14267
• B. 14287
• C. 15287
• D. 13267

Answer 1

The correct option is B

14287

The total number of 5 letter words that can be formed using the seven alphabets such that repetition is allowed is = 7${}^5$

The total number of 5 letter words that can be formed using the seven alphabets such that repetition is not allowed is = ${}^7{C}_5$*5!

So, total number of words that have atleast one letter repeated is = 7${}^5$ - ${}^7{C}_5$*5! = 14287