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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.

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  1. jacobmeir
    • 3 years ago
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    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
    • 3 years ago
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    are the books distinct or are they all the same.

  3. anilorap
    • 3 years ago
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    dont say.. they just books i guess in general

  4. Zarkon
    • 3 years ago
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    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
    • 3 years ago
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    mmmm

  6. jacobmeir
    • 3 years ago
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    wow he got way more arrangements then i did

  7. anilorap
    • 3 years ago
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    well i was doing the combination.. like 6 choose 2 + 6 choose 3 +6 choose 4.. for the first shelf

  8. anilorap
    • 3 years ago
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    |dw:1323670745186:dw|

  9. Zarkon
    • 3 years ago
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    that is just for the 1st shelf?

  10. anilorap
    • 3 years ago
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    yes

  11. anilorap
    • 3 years ago
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    but if i multiply by two... i dont get ur answer tho

  12. Zarkon
    • 3 years ago
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    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
    • 3 years ago
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    *you ARE picking...

  14. Zarkon
    • 3 years ago
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    you could do this...\[{6\choose 2}2!4!+{6\choose 3}3!3!+{6\choose 4}4!2!=2160\]

  15. anilorap
    • 3 years ago
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    ohhh... u r multiplyinggg

  16. anilorap
    • 3 years ago
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    mmm.. wait so i do this

  17. anilorap
    • 3 years ago
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    |dw:1323671159497:dw|

  18. anilorap
    • 3 years ago
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    |dw:1323671255876:dw|

  19. Zarkon
    • 3 years ago
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    \[{6\choose4}=15\]

  20. jacobmeir
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    abcd on top. abc ontop bc on top ac on top. that's more than 3 right there

  24. Zarkon
    • 3 years ago
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    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
    • 3 years ago
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    *ways

  26. anilorap
    • 3 years ago
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    ok,, i got that..im clear up to that point

  27. Zarkon
    • 3 years ago
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    otherwise you have an order and the answer is 2160

  28. anilorap
    • 3 years ago
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    then

  29. anilorap
    • 3 years ago
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    Zarkon i got the first part... but i dont get the second :(

  30. Zarkon
    • 3 years ago
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    what part is that?

  31. anilorap
    • 3 years ago
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    |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
    • 3 years ago
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    it is not 30 it is 15 15*2!4!=15*2*1*4*3*2*1=720 ...

  33. Zarkon
    • 3 years ago
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    720+720+720=2160

  34. anilorap
    • 3 years ago
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    ohhh,, i see what i did wrong... :(... let me do it again

  35. anilorap
    • 3 years ago
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    wowwww,, thanksssss u guys

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