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A world-famous prix fixe menu includes the following choices.

Beverage (choose one): wine, soft drink, coffee, tea, milk, juice, or cappuccino

First course (no choice): baguette, bruschetta, whole roasted garlic, and butter

Second course (choose one): quesadilla, onion soup, salad, Caesar salad, lettuce wedge, spinach salad, or romaine salad

Third course (choose one): rib eye steak, swordfish, rack of lamb, whitefish, grilled chicken, southern fried chicken, lobster, or vegetarian plate
if you choose steak, then choose one of the following: fries, mashed potatoes, creamed corn, spinach, broccoli, or grilled onions

Fourth course (choose one): chocolate cake, cinnamon tart, apple tart, pecan tart, creme brulee, mango sorbet, or chocolate tart

How many different choices are possible?

Respuesta :

Using the fundamental counting theorem, it is found that 107,016 different choices are possible.

Fundamental counting theorem:

States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

  • For the beverage, there are 7 options, hence [tex]n_1 = 7[/tex]
  • For the first course, there are no choice, hence an arrangement of 4 options, that is, [tex]n_2 = 4! = 24[/tex]
  • For the second course, there are 7 options, hence [tex]n_3 = 7[/tex]
  • For the third course, there are 7 non-steak options, plus 6 steak options, hence [tex]n_4 = 13[/tex]
  • For the fourth course, there are 7 choices, hence [tex]n_4 = 7[/tex]

Then, applying the theorem:

[tex]N = 7(24)(7)(13)(7) = 107016 [/tex]

107,016 different choices are possible.

A similar problem is given at https://brainly.com/question/19022577

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