How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once?

gueesstt
Apr 19, 2018

#1**+2 **

How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once?

How many ways can the other 2 letters be chosen where order does not count?

There are 4 ways that the letters an be the same i.e. AA, BB, CC, DD

and there are 4C2=6 ways if the letters are not the same. Making a total of 10 ways.

So there are 10 combinations of letters, how many permutations of these are there

AAA 1 way

AAB, AAC, AAD 3 ways each 3*3=9 ways

ABB, ACC, ADD 3 ways each 3*3=9 ways

ABC, ABD, ACD 3*2=6 ways each 3*6=18ways

1+9+9+18 = 37 ways

Melody
Apr 19, 2018