An English teacher needs to pick 10 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, 4 plays, 6 poetry books, and 6 nonfiction books.
Step 1 of 2: If he wants to include no more than 3 plays, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
To determine the number of different reading schedules, we need to consider the number of ways to select the novels, plays, poetry books, and nonfiction books, as well as the order in which they can be read.
First, let's consider the selection of the novels. There are 4 novels to choose from, and he needs to include all of them in his reading list. Therefore, there is only 1 way to select the novels.
Next, let's consider the selection of the plays. He wants to include no more than 3 plays. This means he can choose 0, 1, 2, or 3 plays from the 4 available plays. We can count the number of ways to do this by using combinations. The number of ways to choose k items from a set of n items is denoted by "n choose k" or represented by the binomial coefficient (nCk). The formula for the binomial coefficient is:
nCk = n! / (k!(n-k)!)
Let's calculate the number of ways to choose 0, 1, 2, or 3 plays:
0 plays: 4C0 = 4! / (0!(4-0)!) = 1
1 play: 4C1 = 4! / (1!(4-1)!) = 4
2 plays: 4C2 = 4! / (2!(4-2)!) = 6
3 plays: 4C3 = 4! / (3!(4-3)!) = 4
Therefore, there are a total of 1 + 4 + 6 + 4 = 15 ways to select the plays.
Moving on to the poetry books, there are 6 available options and he needs to include all of them. So there is only 1 way to select the poetry books.
Lastly, let's consider the nonfiction books. He needs to include 6 out of the 6 available options. Again, there is only 1 way to select the nonfiction books.
To determine the total number of reading schedules, we need to multiply the number of options for each category together:
Number of reading schedules = Number of novel selections * Number of play selections * Number of poetry book selections * Number of nonfiction book selections
Number of reading schedules = 1 * 15 * 1 * 1 = 15
Therefore, there are 15 different reading schedules possible.
Expressing the answer in scientific notation rounding to the hundredths place:
15 = 1.5 x 10^1
So the answer is 1.5 x 10^1 or 15.00.