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