With her box of 64 crayons, your little sister decides to draw a picture of the family: herself, you, and your parents. How many different ways could she find to give you all hair colors?
You don't specify if the hair colours have to be all different, or is not drawing in the hair at all would be a choice.
If all different :
number of ways = 64 x 63 x 62 x 61 = ...
If repeats are allowed:
number of ways = 64^4 = ...
If not drawing the hair at all is a choice, then
start the above with 65
To find the number of different ways your little sister could give each family member a different hair color using her box of 64 crayons, we need to consider that each person can have one of six different hair colors (assuming we have the colors available in the box of crayons).
For the first family member (your little sister), she has all 64 crayon colors to choose from since she can pick any color from the entire set.
For the second family member (you), there are 63 colors remaining because you can't have the same hair color as your little sister.
For the third family member (one of your parents), there are 62 colors remaining because neither you nor your little sister can have the same hair color as one of your parents.
For the fourth family member (the second parent), there are 61 colors remaining because none of you can have the same hair color as the second parent or each other.
Therefore, the total number of different ways your little sister could give each family member a different hair color is calculated as follows:
64 (for the sister) × 63 (for you) × 62 (for the first parent) × 61 (for the second parent) = 16,137,984 different ways.