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 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.

Answer 1

no. of plays narrowed down = 4

no. of books narrowed down = 4+6+6 = 16

no. of books picked = 10

Number of different reading scedules(no more than 3 plays) = Number of schedules with 0 plays + Number of schedules with 1 play + Number of schedules with 2 plays + Number of schedules with 3 plays

= 16C10 + 4C1*16C9 + 4C2*16C8 + 4C3*16C7

= 8008 + 45760 + 77220 + 45760

= 176748

now for each way of selecting 10 books, there would also be 10! permutations

so,

176748*10! = 6.41*10¹¹

please revert if you have any doubts