Question

ABC Paints Ltd. is planning to create different combination of dyes. The research team has decided they will be using five different green dyes, three different red dyes and four different blue dyes. How many combinations of dyes can be created by ABC Paints Ltd., by including at least one blue and one green dye?

• A. 5720
• B. None of the option is correct
• C. 60
• D. 31

Answer 1

The Correct Option is B

Step 1: Red dyes can be chosen freely, including none: \(2^{3}=8\) ways.
Step 2: Green dyes need at least one out of 5: \(2^{5}-1=31\) ways.
Step 3: Blue dyes need at least one out of 4: \(2^{4}-1=15\) ways.
Step 4: Multiply: \(8 \times 31 \times 15 = 3720\), which matches none of the numerical options.
\[ \boxed{\text{None of the option is correct}} \]