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.
help me pls
there are 17C6 ways of choosing the books to go with the 4 poetry books
there are 10! ways of arranging the books in a reading schedule
17C6 * 10! = ?
where did the 6 come from in "17C6"?
To determine the number of different reading schedules possible, we can use the concept of permutations.
Since the teacher wants to include all 4 poetry books, we can treat them as a single entity. Therefore, we only need to consider 9 different items, which are the 5 novels, 5 plays, 7 nonfiction books, and the group of 4 poetry books.
To find the number of different reading schedules, we need to calculate the number of permutations of these 9 items. We can use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of items, and r is the number of items we want to arrange.
In this case, we have 9 items to arrange, and we want to arrange all of them. Therefore, we can use the formula nPr = n!.
Calculating the factorial of 9 gives us:
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880
So, there are 362,880 different ways to arrange the 9 items.
However, we need to express the answer in scientific notation rounded to the hundredths place. Since 362,880 is already in conventional notation, we can write it as 3.63 × 10^5. Rounding to the hundredths place means we round the decimal part to two decimal places.
Thus, the answer is approximately 3.63 × 10^5.