anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Me thinks 4*3*2*1+3*2*1=30
anonymous
  • anonymous
Any thoughts?
anonymous
  • anonymous

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misssunshinexxoxo
  • misssunshinexxoxo
This is a combination. What is 4 times 3?
anonymous
  • anonymous
12
misssunshinexxoxo
  • misssunshinexxoxo
That is the number of different ways you can change the way they are situated
anonymous
  • anonymous
ok
anonymous
  • anonymous
wrong
anonymous
  • anonymous
boo
anonymous
  • anonymous
:(
anonymous
  • anonymous
crying face
SolomonZelman
  • SolomonZelman
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
  • SolomonZelman
it should end up pretty big (not 12 or 11)
anonymous
  • anonymous
4*3*2*1=24 3*2*1=6
anonymous
  • anonymous
so 30
anonymous
  • anonymous
or 60
anonymous
  • anonymous
Ok but answer says 288!!!!!
anonymous
  • anonymous
no entiendo por nada!
SolomonZelman
  • SolomonZelman
yes, because you multiply the permuations by math books, times the permutations by science books
SolomonZelman
  • SolomonZelman
and then multiply by two, because math books can be on top of sceince books or vv
SolomonZelman
  • SolomonZelman
\(\left({\rm 4P4}\times {\rm 3P3}\right)\times 2\)
SolomonZelman
  • SolomonZelman
for each permutation of math books, there is all permutations of science books, and vice versa. that is why you multiply.
SolomonZelman
  • SolomonZelman
and then ×2, because either math books can be on top of science, or the other way around.
anonymous
  • anonymous
You rock!
anonymous
  • anonymous
I need to be careful who I ask
anonymous
  • anonymous
people misinformed all the time
SolomonZelman
  • SolomonZelman
Lol, not really....:) thanks tho:)
SolomonZelman
  • SolomonZelman
Yeah, sometimes answer is wrong, but you have to do a little analysis if the answer makes sense or not.
SolomonZelman
  • SolomonZelman
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
  • anonymous
Yeah. I was nearly running away with 12 which would be a not so correct but intuitive answer.
SolomonZelman
  • SolomonZelman
see what I posted about 11 and 12 just now?
anonymous
  • anonymous
Yeah. Permutations
SolomonZelman
  • SolomonZelman
i will rephrase, there is a typo....
SolomonZelman
  • SolomonZelman
combinations should be "permutations"
SolomonZelman
  • SolomonZelman
But, in any case, now you know.... check your answer to make sense:)
SolomonZelman
  • SolomonZelman
have a good one!
anonymous
  • anonymous
Thanks so much! I'll be writing about you

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