Question

select the correct answer.
a color palette at a paint store has 6 shades of blue. kelsie is choosing 2 shades of blue to paint her room. how many pairs of colors can she pick from the color palette?
a. 12
b. 15
c. 30
d. 720

Explanation:

Step1: Identify combination formula

We use combinations since order of choosing shades does not matter. The formula for combinations is:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=6$ (total shades), $k=2$ (shades to choose)

Step2: Substitute values into formula

$$C(6,2)=\frac{6!}{2!(6-2)!}=\frac{6!}{2!4!}$$

Step3: Simplify the factorial expression

$$\frac{6\times5\times4!}{2\times1\times4!}=\frac{6\times5}{2\times1}$$

Step4: Calculate the final value

$$\frac{30}{2}=15$$

Answer:

B. 15