Question

You have checked out b books from the library, where b is a number greater than 5. You plan to read three of the books and return them at the end of this week. In how many ways can you pick the books you will read first, second, and third?

Answer 1

b3 ways?

Answer 2

What do you mean by b3?

Answer 3

b to the third

Answer 4

Oh, nope. Are you working with permutations and combinations yet?

Answer 5

Nonlinear Functions and Polynomials

Answer 6

(b3 - 3b2 + 2b) ways?

Answer 7

I realy just want to learn how to solve this so i don't have to guess.

Answer 8

Yup

Answer 9

That's correct

Answer 10

My guess was right?

Answer 11

Say for instance b was equal to ten, for your first book you would have 10 choices for your second book you would have 9 choices and for your third book you would have 8 choices

So you would have 10*9*8 = 720 ways of choosing the three books you would read if there were 10 total

Answer 12

So if you had b books, how many choices would you have after you chose one?

Answer 13

b-1

Answer 14

and after you chose that one?

Answer 15

b-2

Answer 16

So how many choices would you have overall?

Answer 17

well, it says be is a number greater than 5. eh,.. 6?

Answer 18

1 * 2 * 3 right?

Answer 19

If you have 3 books of which you can choose two from then you have 3 choices for your first book and then 2 choices for your second book, so overall you have 3*2 = 6 different ways you can choose your two books

Answer 20

So you would have b(b-1)(b-2) ways to choose your books

Answer 21

hey thanks i was kinda right but I don't think my reasoning would work in all circumstanses.

Answer 22

Yup :)