Question

Answer each question below. You may not use a calculator, but you may also leave your answer as a sum, product, and/or quotient of integers. You do not need to simplify. 1. A box contains 16 books, 9 paperbacks and 7 hardcovers. Each book has a different title. (a) How many ways can we select a set of 6 books from the box? (b) How many ways can we select a set of 6 paperbacks? (c) How many ways can we select 6 books that are either all paperback or all hardcovers? (d) How many ways can we select 4 hardcovers and 2 paperbacks? (e) How many ways can we select 6 books include at least one hardcover? 2. 6 different books are to be distributed among the 10 students in a class. A student can receive multiple books; for example, it's possible that one student receives all 6 of them. How many ways are there to distribute the books: (a) How many ways are there to distribute the books? (b) ... if Alice gets at least one book? (c) ... if only Alice, Bob, and Chloe receive books? (d) ... if only Alice, Bob, and Chloe receive books or only Dan and Emily receive books? (e) ... if no student receives more than one book?

Answer 1

we ( Here have Total 16 books the box such that q are paperbacks and 7 are hardcorers. (a) The possible Number of ways use Combinatories because order of here selection does matter not there for 16 16 ways 5 selecting 6-books. we will ) 5 (6) then set of 6-paperbacks is Number of ways 91 9x8X7X6! = 6569-6)! 6!X 3! (0) 84 that (C) set of 6-books such paperback hardcovers i's or all are either all

(9)+(%) Paperback Hardcovers 8ut 7 al (d) we Now and need 4 hardcovers 2-paperbacks 7 Il = 36X35 = 1,260 4 including (e) set of 6 books at least one hardcover which is same as Total Number of ways - No Hardcover - 165)- OR we could use (587+90)-6996) 4(1)(3) + (6) 6)+)(3)

One at a time please.

We used Combinatories in each part.

C(n,r) is also notation for combination