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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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