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Answer :
To solve the problem of how the absence of muffins affected the number of possible combinations for the "commuter special," we need to determine the number of combinations both before and after muffins were unavailable. Here's a step-by-step explanation:
1. Identify Initial Options:
- Pastries: Donut, Brownie, Muffin, Scone, Croissant (5 options)
- Beverages: Coffee, Milk, Tea, Orange Juice (4 options)
- Newspapers: The Times, The Herald, (No Paper) (3 options)
2. Calculate Initial Combinations:
- To find the total number of combinations, multiply the number of options for each category:
[tex]\[
\text{Initial Combinations} = (\text{Number of Pastries}) \times (\text{Number of Beverages}) \times (\text{Number of Papers})
\][/tex]
- With all options available, this calculation becomes:
[tex]\[
5 \times 4 \times 3 = 60
\][/tex]
3. Adjust for Muffin Absence:
- Removing "Muffin" from the pastry choices leaves: Donut, Brownie, Scone, Croissant (4 options).
4. Calculate New Combinations:
- Recalculate the total number of combinations without muffins:
[tex]\[
\text{New Combinations} = (\text{Updated Number of Pastries}) \times (\text{Number of Beverages}) \times (\text{Number of Papers})
\][/tex]
- The new calculation becomes:
[tex]\[
4 \times 4 \times 3 = 48
\][/tex]
5. Determine the Impact:
- Subtract the new number of combinations from the initial number to find the decrease:
[tex]\[
\text{Decrease in Combinations} = \text{Initial Combinations} - \text{New Combinations}
\][/tex]
- Which results in:
[tex]\[
60 - 48 = 12
\][/tex]
Therefore, the absence of muffins decreased the number of possible combinations by 12.
1. Identify Initial Options:
- Pastries: Donut, Brownie, Muffin, Scone, Croissant (5 options)
- Beverages: Coffee, Milk, Tea, Orange Juice (4 options)
- Newspapers: The Times, The Herald, (No Paper) (3 options)
2. Calculate Initial Combinations:
- To find the total number of combinations, multiply the number of options for each category:
[tex]\[
\text{Initial Combinations} = (\text{Number of Pastries}) \times (\text{Number of Beverages}) \times (\text{Number of Papers})
\][/tex]
- With all options available, this calculation becomes:
[tex]\[
5 \times 4 \times 3 = 60
\][/tex]
3. Adjust for Muffin Absence:
- Removing "Muffin" from the pastry choices leaves: Donut, Brownie, Scone, Croissant (4 options).
4. Calculate New Combinations:
- Recalculate the total number of combinations without muffins:
[tex]\[
\text{New Combinations} = (\text{Updated Number of Pastries}) \times (\text{Number of Beverages}) \times (\text{Number of Papers})
\][/tex]
- The new calculation becomes:
[tex]\[
4 \times 4 \times 3 = 48
\][/tex]
5. Determine the Impact:
- Subtract the new number of combinations from the initial number to find the decrease:
[tex]\[
\text{Decrease in Combinations} = \text{Initial Combinations} - \text{New Combinations}
\][/tex]
- Which results in:
[tex]\[
60 - 48 = 12
\][/tex]
Therefore, the absence of muffins decreased the number of possible combinations by 12.
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Rewritten by : Jeany
