(5!)(4!)(2)?
Explain WHY!
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
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
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.
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!
Really?That just is totally a wrong reading of the problem!
"All 5 Computer Science books are arranged on the leftHow 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?
. . 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.