Math Snap

STEP 1

Assumptions1. There are6 different colors red, orange, yellow, green, blue, and violet.
. We are looking for patterns of4 colors.
3. The order of colors in the pattern matters (e.g., red-orange-yellow-green is different from orange-red-green-yellow).
4. A color can be used more than once in a pattern.

STEP 2

This problem is a permutation problem because the order in which the colors are arranged matters. The formula for permutations is$$(n, r) = n^r$$where- $n$ is the total number of options (in this case, the number of colors), and- $r$ is the number of options chosen at a time (in this case, the number of colors in a pattern).

STEP 3

Now, plug in the given values for $n$ and $r$ into the permutation formula.
(6,) =6^

Calculate the number of possible patterns.
$$(6,4) =6^4 =1296$$There are1296 possible patterns of4 colors.