QuestionHow many unique patterns of 4 colors can be formed using the colors red, orange, yellow, green, blue, and violet?
Studdy Solution
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 iswhere- is the total number of options (in this case, the number of colors), and- 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 and into the permutation formula.
(6,) =6^
STEP 4
Calculate the number of possible patterns.
There are1296 possible patterns of4 colors.
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