Math Problem of the Week - Algebra and Up - Dec. 26, 2021 to Jan. 1, 2022

Algebra and Up: 

Question: Clementine dyes her hair a different color every month. The colors she chooses between are blue, red, green, and orange. How many different combinations of colors are there that Clementine could dye her hair month to month for a year? 

Answer: 708,588

Solution: Clementine has 4 hair color options the first month. Since she dyes her hair a different color every month, there are 3 options for each of the rest of the months because the color she used the month before is not an option. So, there are 4 × 3¹¹ = 708,588 different combinations of colors that Clementine could dye her hair from month to month in a year.