Question

An artist with a palette of 12 colors designs a flag with 4 different vertical stripes. find the number of possible flags she can create.

Answer 1

The artist can create 495 possible flags by choosing 4 colors out of the 12-color palette.

Step-by-step explanation:

To find the number of possible flags the artist can create, we need to determine the number of ways to choose different colors for each stripe. Since there are 12 colors on the palette and 4 stripes on the flag, we can use the concept of combinations to calculate the number of possible flags. The number of ways to choose 4 colors out of 12 is given by the formula nCr, where n is the total number of colors and r is the number of colors to choose. Therefore, the number of possible flags the artist can create is 12 choose 4, which can be calculated as follows:

Number of ways = 12! / (4!(12-4)!)

= 12! / (4!8!)

= (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)

= 495.