So I need to arrange 4 science books and 3 math books in such manner that science books are together and math books are together laying on top va each other. How many ways I can do this?

Question

anonymous · Answer

Me thinks 4*3*2*1+3*2*1=30

anonymous · Answer

Any thoughts?

anonymous · Answer

@DaBest21

misssunshinexxoxo · Answer

This is a combination. What is 4 times 3?

anonymous · Answer

12

misssunshinexxoxo · Answer

That is the number of different ways you can change the way they are situated

anonymous · Answer

ok

anonymous · Answer

wrong

anonymous · Answer

boo

anonymous · Answer

:(

anonymous · Answer

crying face

solomonzelman · Answer

This is what I think.

There are 4P4 ways to rearrange the science books, AND
there are 3P3 ways to rearrange the math books.

And all books have to be on top of each other, would mean either math books on top of science books, or science books on top of math books.

that means that all your previous permutations should be multiplied times two.

solomonzelman · Answer

it should end up pretty big (not 12 or 11)

anonymous · Answer

4*3*2*1=24
3*2*1=6

anonymous · Answer

so 30

anonymous · Answer

or 60

anonymous · Answer

Ok but answer says 288!!!!!

anonymous · Answer

no entiendo por nada!

solomonzelman · Answer

yes, because you multiply the permuations by math books, times the permutations by science books

solomonzelman · Answer

and then multiply by two, because math books can be on top of sceince books or vv

solomonzelman · Answer

$\left({\rm 4P4}\times {\rm 3P3}\right)\times 2$

solomonzelman · Answer

for each permutation of math books, there is all permutations of science books, and vice versa. that is why you multiply.

solomonzelman · Answer

and then ×2, because either math books can be on top of science, or the other way around.

anonymous · Answer

You rock!

anonymous · Answer

I need to be careful who I ask

anonymous · Answer

people misinformed all the time

solomonzelman · Answer

Lol, not really....:) thanks tho:)

solomonzelman · Answer

Yeah, sometimes answer is wrong, but you have to do a little analysis if the answer makes sense or not.

solomonzelman · Answer

In this case, for example. How can answer be 11 or 12, if the number of combinations of just the science books alone exceeds that?

anonymous · Answer

Yeah. I was nearly running away with 12 which would be a not so correct but intuitive answer.

solomonzelman · Answer

see what I posted about 11 and 12 just now?

anonymous · Answer

Yeah. Permutations

solomonzelman · Answer

i will rephrase, there is a typo....

solomonzelman · Answer

combinations should be "permutations"

solomonzelman · Answer

But, in any case, now you know.... check your answer to make sense:)

solomonzelman · Answer

have a good one!

anonymous · Answer

Thanks so much! I'll be writing about you