Question

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

Answer 1

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)

Answer 2

are the books distinct or are they all the same.

Answer 3

dont say.. they just books i guess in general

Answer 4

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

Answer 5

mmmm

Answer 6

wow he got way more arrangements then i did

Answer 7

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