An English teacher needs to pick 10 books to put on her reading list for the
next school year, and she needs to plan the order in which they should be
read. She has narrowed down her choices to 5 novels, 5 plays, 4 poetry
books, and 7 nonfiction books.
Step 2 of 2 : If she wants to include all 4 poetry books, how many different
reading schedules are possible? Express your answer in scientific notation
rounding to the hundredths place.
She wants to pick 10 books. She picks all 4 poetry books and therefore needs
to pick 6 more from the 5+5+7=17 other (non-poetry) books.
So she can pick the remaining 6 (non-poetry) books in (17 CHOOSE 6) = 17C6
= 12376 ways.
For each of the 12376 ways to pick the 10 books to read, she can arrange the
order to read them in -- in (10 POSITION 10)=10P10=10!=3628800 ways.
Answer: (17C6)(10!)=12376*3628800 = 4.49×1010
Edwin