Counting rules problem

Hi fellow math lovers,

i took an exam this morning and had an extra credit question which i answered. seeing as i wont get the results until after the weekend, i am hoping someone can verify my answer.

A girl has 3 different colors of nail polish. How many different patterns can she create if she only uses at most 2 colors on each hand?

MY WORK:

First, choose 2 colors for the first hand------------- C(3,2)

Now, each of her five fingers can be either color-----2^5

However, say she chose color A and B, there is the possibility of all being A or all being B, and the other 2 combinations of colors allows for repetition, 6 scenarios all A, A, B, B, C, C, so subtract 3 from the total.

we now have C(3,2) * 2^5 -3

now repeat the same for the other hand and take the Cartesian product of them

FINAL ANSWER:

[C(3,2) * 2^5 -3] ^2

Thanx

berni2723 said:

A girl has 3 different colors of nail polish. How many different patterns can she create if she only uses at most 2 colors on each hand?
MY WORK:
First, choose 2 colors for the first hand------------- C(3,2)
Now, each of her five fingers can be either color-----2^5
However, say she chose color A and B, there is the possibility of all being A or all being B, and the other 2 combinations of colors allows for repetition, 6 scenarios all A, A, B, B, C, C, so subtract 3 from the total.
we now have C(3,2) * 2^5 -3
now repeat the same for the other hand and take the Cartesian product of them
FINAL ANSWER:
[C(3,2) * 2^5 -3] ^2

Click to expand...

That looks well done.