Thread: Counting Methods

The Following Question refers to a set of Five distinct computer science books, three distinct mathematics books, and two distinct art books.

How many different ways can these books be arranged on a shelf if all 5 Computer Science books are arranged on the left and both art books are on the right. ??

This is throwing me off although I am not sure why. I cannot figure out how to make it work no matter what I do. Sorry if it sounds kind of dumb. Any help is appreciated.
Pwr

(5!)(4!)(2)?
Explain WHY!

are the books grouped by category on the shelf?
If the order on the shelf is computer/math/art, and you don't mix the categories, then you have 5! ways to arange the computer books, 3! for the math books, 2! for the art
So in total,
5!3!2!=1440

That was kind of my thought too but... I think what was throwing me off was that the five computer science books HAD to be on the left and the two art books HAD to be on the right. Doesnt that make a difference in the final calculation? or is that just thrown in there to throw people like me?

pwr

Originally Posted by alinailiescu

are the books grouped by category on the shelf?
5!3!2!=1440

NO!
It was not said that the mathematics books must be together.

Hello, pwr_hngry!

There is a set of ten distinct books: five computer science books,
three mathematics books, and two art books.

How many different ways can these books be arranged on a shelf
if all 5 Computer Science books are arranged on the left
and both art books are on the right?

The five computer science books are at the far left.
. . They can be arranged in 5! = 120 ways.

The three math books are in the middle.
. . They can be arranged in 3! = 6 ways.

The two art books are at the far right.
. . They can be arranged in 2! = 2 ways.


Therefore, the ten books can be arranged in: .120 × 6 × 2 .= .1440 ways.

This is great Soroban! I need to use the multiplication principal. The Left and right are distinguished because they force the books into specific categories. Thanks for the great explanation.

Thank you everyone for the help!

Pwr

Originally Posted by Soroban

Therefore, the ten books can be arranged in: .120 × 6 × 2 .= .1440 ways.[/size]

That just is totally a wrong reading of the problem!
As I read first the computer science books were a block with the mathematics books were to the left of the art books: (5!)(4!)(2).
However, if we read the problem as if computer science books are not necessarily together the then answer is: (8!)(2).

Can any of you tell me why anyone should read this problem as implying that the three kinds of books should remain as a block?

If that is the case surely the answer is (2)(5!)(3!)(2!)

Hello, Plato!

That just is totally a wrong reading of the problem!

Really?

How many different ways can these books be arranged on a shelf
if all 5 Computer Science books are arranged on the left
and both art books are on the right?

"All 5 Computer Science books are arranged on the left
. . and both Art books are on the right."
I get only one interpretation of these instructions.
. . They are placed in "blocks" by subject.

If they meant "the Computer Science books are (somewhere) to the left of the Art books",
. . they are morally obligated to say so ... clearly.