Tuesday

July 22, 2014

July 22, 2014

Posted by **lizzie** on Thursday, April 22, 2010 at 10:45am.

a) The books are different and the boxes are different?

b) The books are the same and the boxes are different?

c) The books are different and the boxes are the same?

d) The books are the same and the boxes are the same?

- math -
**PsyDAG**, Thursday, April 22, 2010 at 11:31amI'm confused as to what you mean by the "same" and "different." Can you rephrase the problem in a new post?

- math -
**Reiny**, Thursday, April 22, 2010 at 12:26pmInteresting question.

let's call our boxes A,B, and C

and our books 1,2,3,4, and 5

let's do b) first

our books are all the same, so we will just separate them into 3 piles adding to 5

1 1 3

1 2 2

1 3 1

2 1 2

2 2 1

3 1 1

so if our first column is box A, second column is B etc

then there are 6 ways.

d) if the boxes are the same as well, then isn't 1 2 2 the same as 2 1 2?

so there are only 2 distinct ways , namely 1 1 3 and 1 2 2, since the order does not matter.

a) notice in b) we found there are 6 ways to put identical books in 3 distinct boxes.

Now suppose that all the books are different.

Couldn't these 5 books now be**arranged**in 5! or 24 ways, without changing the count in the 3 distinct boxes?

so with all books different and boxes different, the number of ways would be 6x24 or 144 ways.

That leaves c)

see if you can reason it out.

**Related Questions**

math - Flora’s class collected 236 books. They are placing the books in boxes. ...

MATHS - Mrs.Koh purchased new books for the school library, of which 6 were ...

math - A student has 4 English books,3 math books,and 5 history books.In how ...

pre calc - A math teacher uses four algebra books, two geometry books, and three...

Math - John has 4 math books, 6 biology books,, and 8 statistics books to ...

Algebra - A moving Company weighs 20 boxes you have packed that contain either ...

Math (Sorry, Forgot to add Part B) - The Pleasant Valley Library is moving to a ...

math - MEghan had 36 books in her locker. Some were library books, text books ...

math - lara arranged the books in her bookshelf by size. 2/10 of the books were ...

Math - Meredith took 15 minutes to unpack 4 boxes of books. If she unpacked a ...