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[tex]\binom{8}{3} = \frac{8!}{3! \times 5!} = 56[/tex] different side dishes.
The number of ways steak can be selected is =[tex]\binom{5}{1} = \frac{5!}{1! 4!} =5[/tex]
The number of ways toppings can be chosen is = [tex]\binom{8}{3} = \frac{8!}{3! 5!} = 56[/tex]
The number of ways side dishes can be chosen = [tex]\binom{7}{4} = \frac{7!}{4!3!} = 35.[/tex]
Therefore the total number of ways that the customer can order the smothered steak dinner is
= 5 × 56 × 35 = 9800.
