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?\n4\n6\n10\n15
Answer
Explanation:
Step1: Determine remaining colors to choose
Since green is already fixed and we need 4 - color combinations, we need to choose 3 colors from the remaining 5 colors (red, yellow, purple, orange, blue).
Step2: Use combination formula
The combination formula is $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 5$ (remaining colors) and $k=3$ (number of 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