select the correct answer.\na color palette at a paint store has 6 shades of blue. kelsie is choosing 2…

Explanation:

Step1: Identify the problem type

This is a combination problem since the order of choosing the shades does not matter. The formula for combinations is ( C(n, k)=\frac{n!}{k!(n - k)!} ), where ( n ) is the total number of items, and ( k ) is the number of items to choose. Here, ( n = 6 ) (total shades of blue) and ( k=2 ) (shades to choose).

Step2: Calculate the factorial values

First, calculate ( n!=6! = 6\times5\times4\times3\times2\times1=720 ), ( k!=2! = 2\times1 = 2 ), and ( (n - k)!=(6 - 2)!=4! = 4\times3\times2\times1 = 24 ).

Step3: Substitute into the combination formula

Substitute the values into the formula: ( C(6, 2)=\frac{6!}{2!(6 - 2)!}=\frac{720}{2\times24} ).

Step4: Simplify the expression

Simplify the denominator: ( 2\times24 = 48 ). Then, ( \frac{720}{48}=15 ).

Answer:

B. 15