Question 549939: There are 2 work each of 3 volumes and 2 work each of 2 volumes. In how many ways can the 10 books be placed on a shelf so that the volumes of same work are not separated ?
Answer- 3456
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 4 different works.
on a shelf, they can be arranged in 24 ways.
using the permutation formula, this works out to be:
4! = 4*3*2*1 = 24
each of the 3 volume works can be arranged in 6 ways.
using the permutation formula, this works out to be:
3! = 3*2*1 = 6
each of the 2 volume works can be arranged in 2 ways.
using the permutation formula, this works out to be:
2! = 2*1 = 2
for each of the 24 possible arrangements of works, you have 6 * 6 * 2 * 2 possible arrangements within each work.
this comes out to be 24 * 6 * 6 * 2 * 2 = 3456
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