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Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.) How many different card designs are possible?

Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 22 sizes, 44 colors, 77 phrases, and 44 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)\newlineHow many different card designs are possible?

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Full solution

Q. Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 22 sizes, 44 colors, 77 phrases, and 44 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)\newlineHow many different card designs are possible?
  1. Multiply Choices for Each Category: First, we need to multiply the number of choices for each category together.
  2. Calculate Total Choices: So, we do 22 sizes times 44 colors times 77 phrases times 44 pictures.
  3. Final Result: That's 2×4×7×42 \times 4 \times 7 \times 4.
  4. Final Result: That's 2×4×7×42 \times 4 \times 7 \times 4.Calculating that gives us 2×4=82 \times 4 = 8, then 8×7=568 \times 7 = 56, and finally 56×4=22456 \times 4 = 224.
  5. Final Result: That's 2×4×7×42 \times 4 \times 7 \times 4.Calculating that gives us 2×4=82 \times 4 = 8, then 8×7=568 \times 7 = 56, and finally 56×4=22456 \times 4 = 224.So, Paula can make 224224 different card designs.

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