Case 2 : 4 letters Repetition is allowed
In this case , bucket 1 can have any of the 4 letters “ C , A , R , D ” . That is 4 choices
Bucket 2 can also have any of the 4 letters , since repetition is allowed , that is 2 choices
Bucket 3 can also have any of the 4 letters , since repetition is allowed , that is 2 choices
Bucket 4 can also have any of the 4 letters , since repetition is allowed , that is 2 choices
If you multiple all these choices : 4 * 4 * 4 * 4 , you will get the number of possible 4 letter words with “ C A R D ” with repetition .
Thus number of possible 4 letter words are : 4 * 4 * 4 * 4 = 256 words when repetition is allowed .
Case 3 : 2 letters Repetition is not allowed
In this case , bucket 1 can have any of the 4 letters “ C , A , R , D ” . That is 4 choices
Bucket 2 can have any of the remaining 3 letters as one letter is now inside bucket 1 , that is 3 choices
There is no bucket 3 & 4 , as we have to find 2 letters word such as CA , CD , RD , RA etc
If you multiple all these choices : 4 * 3 , you will get the number of possible 2 letter words with “ C A R D ”, without repetition
Thus number of possible 2 letter words are : 4 * 3 repetition is not allowed .
= 12 words when