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In how many different ways can a person select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books?

a). 15

b). 105

c). 3

d). 22

Respuesta :

Answer:

[tex] Ways = 3*5*7= 105[/tex]

And that's equivalent to:

[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]

Where C represent the term combinatory defined as:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

And then the number of ways to select the three books are 105, and the best option would be:

b). 105

Step-by-step explanation:

For this case we can use the multplication principle of counting or sometimes called the product rule.

We have a total of 3 novels, 5 biographies and 7 self-help books. And we can find the number of ways that a person can select the three books with theis product:

[tex] Ways = 3*5*7= 105[/tex]

And that's equivalent to:

[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]

Where C represent the term combinatory defined as:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

And then the number of ways to select the three books are 105, and the best option would be:

b). 105

facundo3141592

We want to see in how many different ways a person can select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books, the correct option is b: 105.

To get the numbe of different ways, the first thing we need to do is find the selections.

Here we have 3 selections:

  • Novel selection.
  • Biography selection
  • Self-help selection.

Now we need to find the number of options for each of these selections, and just multiply the numbers of options.

we have:

  • Novel selection: 3 options
  • Biography selection: 5 options
  • Self-help selection: 7 options

Number of different ways of selecting = 3*5*7 = 105

So the correct option is b.

If you want to learn more, you can read:

https://brainly.com/question/3349431

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