Question

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?
○ 4
○ 6
○ 10
○ 15

Explanation:

Step1: Fix green, count remaining colors

Total non-green colors: $6 - 1 = 5$

Step2: Choose 3 from 5 colors

Use combination formula: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$, where $n=5$, $k=3$
$\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5\times4\times3!}{3!\times2\times1} = 10$

Answer:

10