contestada

An English teacher needs to pick 6 books to put on his reading list for the next school year, and he needs to plan the order in which they should be read. He has narrowed down his choices to 13 novels, 8 plays, and 11 nonfiction books. If he wants to include an equal number of novels, plays, and nonfiction books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

Respuesta :

Using arrangements and combination, it is found that there are [tex]8.65 \times 10^7[/tex] different schedules possible.

-------------------------------------------

  • First, we find the number of choices for the books.
  • The order in which the books are chosen is not important, which means that the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

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

-------------------------------------------

  • 2 books are chosen from each set.
  • 2 from 13 novels, 2 from 8 plays, 2 from 11 nonfiction. Thus:

[tex]T = C_{13,2}C_{8,2}C_{11,2} = \frac{13!}{2!11!} \times \frac{8!}{2!6!} \times \frac{11!}{2!9!} = 120120[/tex]

-------------------------------------------

  • After the books are chosen, then the order is important, as they are arranged.
  • The number of ways n elements can be arranged is given by [tex]n![/tex]
  • Thus, considering the order, the total number of ways is:

[tex]6!(120120) = 720(120120) = 86486400[/tex]

  • In scientific notation, [tex]8.65 \times 10^7[/tex] ways.

A similar problem is given at https://brainly.com/question/23302762

Otras preguntas