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Answer :
Sure! Let's break down the process to determine how the absence of muffins affected the number of possible "commuter special" combinations at the deli.
1. Identify the options available:
- Pastry options: Donut, Brownie, Muffin, Scone, and Croissant. That's a total of 5 pastry options.
- Beverage options: Coffee, Milk, Tea, and Orange Juice. This gives us 4 beverage choices.
- Paper options: The Times and The Herald provide us with 2 newspaper choices.
2. Calculate the initial number of combinations:
To find the total number of combinations, we multiply the number of options for pastries, beverages, and papers:
[tex]\[
5 \text{ pastries} \times 4 \text{ beverages} \times 2 \text{ papers} = 40 \text{ combinations}
\][/tex]
3. Consider the scenario when muffins are unavailable:
When there are no muffins, the number of available pastry options reduces by 1, leaving us with:
- Pastry options: Donut, Brownie, Scone, and Croissant, which totals 4 pastry choices.
4. Calculate the new number of combinations without muffins:
[tex]\[
4 \text{ pastries} \times 4 \text{ beverages} \times 2 \text{ papers} = 32 \text{ combinations}
\][/tex]
5. Determine how the number of combinations changed:
The decrease in the number of combinations is the difference between the initial and new combinations:
[tex]\[
40 \text{ initial combinations} - 32 \text{ combinations without muffin} = 8 \text{ fewer combinations}
\][/tex]
Therefore, the absence of muffins decreased the number of possible combinations by 8.
1. Identify the options available:
- Pastry options: Donut, Brownie, Muffin, Scone, and Croissant. That's a total of 5 pastry options.
- Beverage options: Coffee, Milk, Tea, and Orange Juice. This gives us 4 beverage choices.
- Paper options: The Times and The Herald provide us with 2 newspaper choices.
2. Calculate the initial number of combinations:
To find the total number of combinations, we multiply the number of options for pastries, beverages, and papers:
[tex]\[
5 \text{ pastries} \times 4 \text{ beverages} \times 2 \text{ papers} = 40 \text{ combinations}
\][/tex]
3. Consider the scenario when muffins are unavailable:
When there are no muffins, the number of available pastry options reduces by 1, leaving us with:
- Pastry options: Donut, Brownie, Scone, and Croissant, which totals 4 pastry choices.
4. Calculate the new number of combinations without muffins:
[tex]\[
4 \text{ pastries} \times 4 \text{ beverages} \times 2 \text{ papers} = 32 \text{ combinations}
\][/tex]
5. Determine how the number of combinations changed:
The decrease in the number of combinations is the difference between the initial and new combinations:
[tex]\[
40 \text{ initial combinations} - 32 \text{ combinations without muffin} = 8 \text{ fewer combinations}
\][/tex]
Therefore, the absence of muffins decreased the number of possible combinations by 8.
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Rewritten by : Jeany
