A restaraunt offers a dinner special that lets you choose from 10 entrees, 8 side dishes, and 13 deserts. You can choose one entree, two side dishes, and one desert.
How many different meals are possible?
10c1*8c2*13c1=3640
To calculate the total number of different meals possible, we need to multiply the number of options for each category together.
Number of options for entrees: 10
Number of options for side dishes: 8 choose 2 (combination) = (8!)/((2!(8-2)!)) = (8!)/(2!6!) = (8x7)/(2x1) = 28
Number of options for desserts: 13
Total number of different meals = Number of options for entrees × Number of options for side dishes × Number of options for desserts
= 10 × 28 × 13
= 3640
Therefore, there are 3640 different meals possible.
To find the total number of different meals that are possible, we need to multiply the number of choices for each category together.
1. Entrees: The restaurant offers 10 different entrees to choose from.
2. Side dishes: You can choose two side dishes. Since there are 8 side dishes available, we can calculate the number of combinations using the combination formula (nCr), where n is the total number of options and r is the number of choices:
Number of combinations = 8C2 = 8! / (2! * (8 - 2)!) = 28
So, there are a total of 28 combinations for the side dishes.
3. Desserts: There are 13 desserts available to choose from.
To find the total number of different meals possible, we multiply the number of choices for each category together:
Total number of different meals = 10 (entrees) x 28 (side dish combinations) x 13 (desserts)
Total number of different meals = 3,640.
Therefore, there are 3,640 different meals possible based on the given choices.