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Garcia's Grill offers 8 side dishes, 3 types of steak, and 7 toppings. How many different...

Garcia's Grill offers 8 side dishes, 3 types of steak, and 7 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 2 different toppings and 4 different side dishes?

Math   Statistics-And-Probability   
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Answer #1

Garcia's Grill offers 8 side dishes, 3 types of steak and 7 toppings

Now a smothered steak dinner consists of 1 steak served with 2 different toppings and 4 different side dishes

To find out how many different smothered steak dinners can be made we will use combinatorics

Number of ways the 1 steak can be selected from 3 types of steaks = 3C1= 3 [as we are selecting 1 out of 3]

Number of ways 4 different side dishes can be selected from 8 types of side dishes= 8C4= 70 [as we are selecting 4 out of 8]

Number of ways 2 different toppings can be selected from 7 types of toppings= 7C2= 21 [as we are selecting 2 out of 7]

To find how many different smothered steak dinners can be made we multiply number of ways each item can be selected

Number of different smothered steak dinners can be made = 3C1 * 8C4 * 7C2 = 3*70*21 = 4410

Answer: 4410 different smothered steak dinners can be made

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