Question

Garcia's Grill offers 77 side dishes, 55 types of steak, and 88 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 33 different toppings and 44 different side dishes?

Answer 1

Answer:

Therefore the total number of ways that the customer can order the smothered steak dinner  is 9800.

Step-by-step explanation:

There are 7 side dishes, and  types of stake and 8 toppings.

The customer will have a smothered steak dinner.

The smothered steak dinner will consist of steak and 3 different toppings and 4$\binom{8}{3} = \frac{8!}{3! \times 5!} = 56$ different side dishes.

The number of ways steak can be selected is =$\binom{5}{1} = \frac{5!}{1! 4!} =5$

The number of ways toppings can be chosen is  = $\binom{8}{3} = \frac{8!}{3! 5!} = 56$

The number of ways side dishes can be chosen = $\binom{7}{4} = \frac{7!}{4!3!} = 35.$

Therefore the total number of ways that the customer can order the smothered steak dinner  is

= 5 × 56 × 35  = 9800.