Question

An English teacher needs to pick 9 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 4 novels, 6 plays, 5 poetry books, and 5nonfiction books.Step 2 of 2 :If he wants to include all 4novels, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

Answer:   $4.37\times10^3$

Step-by-step explanation:

Given : Number of choices for novels = 4

Number of choices for plays = 6

Number of choices for poetry books = 5

Number of choices for nonfiction books = 5

Total books =4+6+5+5=20

If he wants to include all 4 novels, then the number of books left to select = 9-4=5

Remaining choices for books = 20-4=16

Number of combinations of n things taking r at a time : $\dfrac{n!}{r!(n-r)!}$

Then, the number of different reading schedules are possible :_

$^4C_4\times^{16}C_5\\\\=\dfrac{4!}{4!(4-4)!}\times\dfrac{16!}{5!(16-5)!}\\\\=(1)\times\dfrac{16\times15\times14\times13\times12\times11!}{120\times11!}\\\\=4368=4.368\times10^3\approx4.37\times10^3$

Hence, the required answer is $4.37\times10^3$.