Question

7. An English teacher needs to pick 13 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, 7 plays, 7 poetry books, and 5 nonfiction books.

Step 1 of 2: If she wants to include no more than 2 nonfiction books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

___×10^

Step 2 of 2: If she wants to include all 7 poetry books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

___x10^

Answer 1

Here 13 books are to be selected from

5 novels,

7 plays,

7 poetry books &

5 nonfiction

step-1with no more than 2 nonfiction books

ie Combinations with 0 non fiction books +  Combinations with 1 non fiction books +  Combinations with 2 non fiction books

= (5+7+7) C 13 + (5+7+7) C 12 * 5C1 + (5+7+7) C 11 * 5C2

=1034892 =1.035*10^6

step-2

If she wants to include all 7 poetry books

then combinations for selecting 13 books have the choice for rest of the 6 books from remaining 17 books

So the total selections are

= 7C7 * 17C6

=12376

=1.24*10^4

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!