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

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

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} = (8!)/(3! * 5!) = 56` different side dishes.

The number of ways steak can be selected is =
`\binom{5}{1} = (5!)/(1! 4!) =5`

The number of ways toppings can be chosen is =
`\binom{8}{3} = (8!)/(3! 5!) = 56`

The number of ways side dishes can be chosen =
`\binom{7}{4} = (7!)/(4!3!) = 35.`

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

= 5 × 56 × 35 = 9800.