## anilorap 3 years ago in how many ways can 6 books be arrange on two shelves, such that there is at least 2 books on each shelve.

1. jacobmeir

from 6 choose 2 plus from 6 choose 3 plus from 6 choose 4 = 6*5/2 +6*4*3/(3*2) +6*4*3*2/(4*3*2)

2. Zarkon

are the books distinct or are they all the same.

3. anilorap

dont say.. they just books i guess in general

4. Zarkon

then there are 3 main ways to put the books on the shelf xx|xxxx xxx|xxx xxxx|xx each of which can be arranged 6! ways giving us a total of 6!*3=2160

5. anilorap

mmmm

6. jacobmeir

wow he got way more arrangements then i did

7. anilorap

well i was doing the combination.. like 6 choose 2 + 6 choose 3 +6 choose 4.. for the first shelf

8. anilorap

|dw:1323670745186:dw|

9. Zarkon

that is just for the 1st shelf?

10. anilorap

yes

11. anilorap

but if i multiply by two... i dont get ur answer tho

12. Zarkon

you par picking the number of books to be on the first shelf....you still need to arrange the books once you pick the number you want

13. Zarkon

*you ARE picking...

14. Zarkon

you could do this...\[{6\choose 2}2!4!+{6\choose 3}3!3!+{6\choose 4}4!2!=2160\]

15. anilorap

ohhh... u r multiplyinggg

16. anilorap

mmm.. wait so i do this

17. anilorap

|dw:1323671159497:dw|

18. anilorap

|dw:1323671255876:dw|

19. Zarkon

\[{6\choose4}=15\]

20. jacobmeir

from the way you wrote the problem, I doubt the arrangment on the shelf matters. I'd say the answer is 15 +20 +15 =50

21. anilorap

the problem says: Ali has six books and she wants to put them on two shelves, such that there is at least two books on each shelf. in how many ways can she do this?

22. Zarkon

it should matter...when you are choosing you are selecting 2 or 3 or 4 specific books to be on the first shelf....if you are doing this where order does not matter then there are only 3 ways to do it.

23. jacobmeir

abcd on top. abc ontop bc on top ac on top. that's more than 3 right there

24. Zarkon

2 books on the first 4 on the sec 3 books on the first 3 on the sec 4 books on the first 2 on the sec 3 wyas

25. Zarkon

*ways

26. anilorap

ok,, i got that..im clear up to that point

27. Zarkon

otherwise you have an order and the answer is 2160

28. anilorap

then

29. anilorap

Zarkon i got the first part... but i dont get the second :(

30. Zarkon

what part is that?

31. anilorap

|dw:1323671862157:dw| this part is correct u said... now i need to arrange them and u told me |dw:1323671932238:dw| to do this..

32. Zarkon

it is not 30 it is 15 15*2!4!=15*2*1*4*3*2*1=720 ...

33. Zarkon

720+720+720=2160

34. anilorap

ohhh,, i see what i did wrong... :(... let me do it again

35. anilorap

wowwww,, thanksssss u guys