Question

lliana 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

Answer 1

Answer: i believe the answer is 4

Step-by-step explanation:

she can have

green red yellow purple

green yellow purple orange

green red purple orange

green red yellow orange

i couldn't see anymore combos but i could be wrong

Answer 2

Answer:  10

Step-by-step explanation:

Given : lliana is painting a picture. She has green, red, yellow, purple, orange, and blue paint.

Total number of colors = 6

If order does not matter, then we use combinations.

The number of combinations of n things taken r at a time :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

If green is already selected , then the remaining number of colors to choose  = 3 out of 5  ( red, yellow, purple, orange, and blue paint.)

$^5C_3=\dfrac{5!}{3!(5-3)!}\\\\=\dfrac{5\times4\times3!}{3!2!}=10$

The number of ways can she pick four colors if green must be one of them = 10.