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Olivia has enter a buffet line in which he chooses one kind of meat two kinds of vegatables and one dessert if the order of the food items are not important how many different meals can she choose meat: duck beef chicken mutton Vegatables: baked beams corn potatoes tomatoes spinach lettuce dessert brownies chocalate cake ice cream and vanilla pudding

Sagot :

Using the Fundamental Counting Theorem, it is found that she can choose 180 different meals.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, 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 meat, there are 3 outcomes, hence [tex]n_1 = 3[/tex].
  • For the two vegetables, 2 are taken from a set of 6, hence, applying the combination formula, [tex]n_2 = C_{6,2} = \frac{6!}{2!4!} = 15[/tex].
  • For the dessert, there are 4 outcomes, hence [tex]n_3 = 4[/tex].

Then:

[tex]N = n_1n_2n_3 = 3(15)(4) = 180[/tex]

She can choose 180 different meals.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866

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