contestada

Please help with algebra


In how many ways could you choose 3 side dishes from a menu that offers 5 vegetable side dishes

and 3 starches if you want at least one vegetable and one starch?

Respuesta :

Using the Fundamental Counting Theorem, it is found that there are 90 ways to choose the three side dishes.

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 vegetable, there are 5 options, hence [tex]n_1 = 5[/tex].
  • For the starch, there are 3 options, hence [tex]n_2 = 3[/tex].
  • The remaining dish is free, which means that there are 5 + 3 - 2 = 6 options, hence [tex]n_3 = 6[/tex].

Then:

N = 5 x 3 x 6 = 90.

There are 90 ways to choose the three side dishes.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

Otras preguntas