Problem 7
Answer: 60
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Step-by-step explanation:
Let's say we only worried about the colors and the sizes. We have 3 colors and 4 sizes, giving 3*4 = 12 different combos. Think of a table that's 3 rows and 4 columns. We'd have 12 inner cells. Each cell represents a different combo.
This idea extends out to not just two factors, but we can have as many as we want. In short, we simply multiply the values given to us: 3*4*5 = 12*5 = 60 different t-shirts. Your math textbook or your teacher may refer to this method as the counting principle, though they may use another term.
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Problem 8
Answer: 224
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Step-by-step explanation:
We use the same idea as problem 7.
4*7*8 = 28*8 = 224 different coats
As an alternative, you can draw out a tree diagram. However, these types of drawings can get very cluttered.
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Problem 9
Answer: 5040
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Step-by-step explanation:
We'll use the same idea as before.
We have 10 choices for the first slot (0 through 9)
Once the first digit is selected, then we have 10-1 = 9 choices left for slot two
Then slot three has 9-1 = 8 choices, and so on.
We have this countdown: 10, 9, 8, 7
The countdown stops once we filled out the four slots. Multiply these values to get the final answer: 10*9*8*7 = 5040. The multiplication step is where we refer to the ideas mentioned in problems 7 and 8 earlier.
Keep in mind that this allows for 0 to be in the first slot. So a number like "0179" is one possibility here. If 0 is not allowed for the first digit, then you'll compute the answer like so:
9*9*8*7 = 4536
This is because we have 9 choices for the first digit, then 9 for the next, and so on. I would ask your teacher for clarification on this one.