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 5 novels, 6 plays, 5 poetry books, and 6 nonfiction books.

Question

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 5 novels, 6 plays, 5 poetry books, and 6 nonfiction books.

Step 1 of 2 :  If he wants to include no more than 4 plays, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

I know it starts with 6c0 x ___ + 6c1 x ____ = 6c2 x ______ + 6c3 x _______ + 6c4

Reiny · Answer

number of ways to choose 10 from 22
= C(22,10)
what can't we have:
choosing 5 plays + choosing 6 plays
= C(6,5)xC(16,5) + C(6,6)xC(16,4)

number of ways = C(22,10) - ( C(6,5)xC(16,5) + C(6,6)xC(16,4) )
= 646646 - (26208+1820)
= 618618
or in scientific: 6.19x10^5 (but why write it that way)

long way:
C(6,0)xC(16,10) + C(6,1)xC(16,9) + ... + C(6,4)xC(16,6)
= 618618

Anonymous · Answer

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, 3 poetry books, and 5 nonfiction books.