Mathematics, 18.05.2021 19:20 shawdyylinda

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 13 novels, 17 plays, and 13 nonfiction books. If he wants to include an equal number of novels, plays, and nonfiction books, how many different reading schedules are possible

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Answer from: jgunt8277

Different schedule Possible = 55,621,280

Step-by-step explanation:

Given - 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 13 novels, 17 plays, and 13 nonfiction books.

To find - If he wants to include an equal number of novels, plays, and nonfiction books, how many different reading schedules are possible ?

Formula used -

Number of combinations of n things taking r at a time : $^{n}C_{r}$ = $\frac{n!}{r! (n-r)!}$

Proof -

Given that, An English teacher needs to pick 9 books and wants to include equal number of novels, plays, and nonfiction books

i.e. he will Choose

3 books from Novels

3 books from Plays

3 books from Non-fiction books

Now,

Given that,

Total number of novel = 13

Total number of plays = 17

Total number of non-fiction books = 13

So,

Different schedule Possible = $^{13}C_{3}* ^{17}C_{3}*^{13}C_{3}$

= $\frac{13!}{3! (13-3)!}* \frac{17!}{3! (17-3)!}* \frac{13!}{3! (13-3)!}$

= $\frac{13!}{3! (10)!}* \frac{17!}{3! (14)!}* \frac{13!}{3! (10)!}$

= $\frac{13(12)(11)10!}{3! (10)!}* \frac{17(16)(15)14!}{3! (14)!}* \frac{13(12)(11)10!}{3! (10)!}$

= $\frac{13(12)(11)}{3(2)(1)}* \frac{17(16)(15)}{3(2)(1)}* \frac{13(12)(11)}{3(2)(1)}$

= {13(2)(11)}*{17(8)(5)}* {13(2)(11)}

= 55,621,280

⇒Different schedule Possible = 55,621,280

Answer from: Quest

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!

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grab rope, tie a loop-de-loop, put it around ur neck, now jump while its tied to a high place. now your shoes are cool.

step-by-step explanation:

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