Permutation

Question

There are 4 letters A B C and D. Each letter have 3 variety of color Red, Yellow and Green.
So basically the letters goes as

red A, yellow A, green A,
red B, yellow B, green B
red C, yellow C, green C
red D, yellow D, green D

How many permutations can there be if each permutation should have only 3 letters which is different from each other. Example;
(Red A, Red B, Red C),
(Red A, Red B, Red D),
(Yellow A, Red C, Green D)
(yellow D, green B, green C) and so on..

I would greatly appreciate if you can give me the arrangements too. Thanks

Answer 1

Let's first just worry about letters. Let's look at all combinations that start with A:

 

ABC

ABD

ACD

 

So, that is 3 possibilities. But, I can equally do this for letter combinations that begin with B, C and D respectively. So, in just considering letters, I get 3 X 4 = 12 combinations.

 

How about colors? Let's just consider one of the letter permutations above. Let's consider say ABC. For this particular combination, if R = Red, Y = Yellow and G = Green, we can assign colors to ABC in the following possible ways: RYG, RGY, YRG, YGR, GYR, and GRY or 6 combinations. So, this is 6 possibilities for just ABC. But, we have 12 letter combinations. So, I think every possible permutation is (12 letter combinations) X (6 color permutations) = 72

 

This is what I get. Combinatorics is not my strongest suit though. :-)