## anonymous one year ago 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?

1. anonymous

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

2. anonymous

Any thoughts?

3. anonymous

@DaBest21

4. misssunshinexxoxo

This is a combination. What is 4 times 3?

5. anonymous

12

6. misssunshinexxoxo

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

7. anonymous

ok

8. anonymous

wrong

9. anonymous

boo

10. anonymous

:(

11. anonymous

crying face

12. 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.

13. SolomonZelman

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

14. anonymous

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

15. anonymous

so 30

16. anonymous

or 60

17. anonymous

18. anonymous

19. SolomonZelman

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

20. SolomonZelman

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

21. SolomonZelman

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

22. SolomonZelman

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

23. SolomonZelman

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

24. anonymous

You rock!

25. anonymous

I need to be careful who I ask

26. anonymous

people misinformed all the time

27. SolomonZelman

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

28. SolomonZelman

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

29. 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?

30. anonymous

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

31. SolomonZelman

see what I posted about 11 and 12 just now?

32. anonymous

Yeah. Permutations

33. SolomonZelman

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

34. SolomonZelman

combinations should be "permutations"

35. SolomonZelman

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

36. SolomonZelman

have a good one!

37. anonymous

Thanks so much! I'll be writing about you