SOLUTION: In how many ways can 4 large books, 3 medium- size books, and 2 small books, be placed on a shelf so that all books of the same size are together

Algebra ->  Permutations -> SOLUTION: In how many ways can 4 large books, 3 medium- size books, and 2 small books, be placed on a shelf so that all books of the same size are together      Log On


   

Question 925983: In how many ways can 4 large books, 3 medium- size books, and 2 small books, be placed on a shelf so that all books of the same size are together
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
let as assume 4 large books as 1 unit and 3 medium- size book as another unit and 2 small books as one more unit
these 3 units can be arranged in 3! ways
first unit consist of 4 large books. these books can be internally arranged in 4! ways
second unit consist of 3 medium sized books. these books can be internally arranged in 3! ways
third unit consist of 2 small books. these books can be internally arranged in 2! ways
Total no of ways = 3! * 4!*3!*2!
3 ! = 3x2x1 = 6
4!~=4x3x2x1 = 24
2! = 2x1 =2
result = 3! * 4!*3!*2!
= 6*24*6*2
=1728