A knitted hat pattern comes in 5 styles with 3 stitch options and 4sizes, and there are 7 yarns appropriate for the hat. Disregarding the stitch options, how many different hats can be made?

Question

A knitted hat pattern comes in 5 styles with 3 stitch options and 4sizes, and there are 7 yarns appropriate for the hat. Disregarding the stitch options, how many different hats can be made?

Answer 1

The fundamental counting principle states that if there are n(A) outcomes in event A and n(B) outcomes in event B, then there are n(A)×n(B) outcomes in event A and event B combined.

We can use this rule to determine how many different hats can be made if there are 5 possible outcomes in style options, 4 possible sizes in size options, and 7 possible outcomes in yarn options (Remember, we are told to disregard the stitch options, so we will not consider the 3 stitch options).

By finding the product of the number of possible outcomes in all 3 events combined, we find that there are 5*4*7 ways that different hats can be made.

Hope this helps!