iliana is painting a picture. she has green, red, yellow, purple, orange, and blue paint. she wants her…

iliana is painting a picture. she has green, red, yellow, purple, orange, and blue paint. she wants her painting to have four different colors. if order does not matter, in how many ways can she pick four colors if green must be one of them?\no 4\no 6\no 10\no 15

iliana is painting a picture. she has green, red, yellow, purple, orange, and blue paint. she wants her painting to have four different colors. if order does not matter, in how many ways can she pick four colors if green must be one of them?\no 4\no 6\no 10\no 15

Answer

Explanation:

Step1: Fix green color

Since green is already fixed, we need to choose 3 colors from the remaining 5 colors.

Step2: Use combination formula

The combination formula is $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 5$ (remaining colors) and $k=3$ (colors to choose). $C(5,3)=\frac{5!}{3!(5 - 3)!}=\frac{5!}{3!2!}=\frac{5\times4\times3!}{3!\times2\times1}=10$

Answer:

10