Utsav! Arrange your bookshelf.

Probability Level 4

How many ways can I arrange 10 10 different books on 3 3 different shelves such that none should be left empty? Order of books on each shelf matters .

Tell me the number of ways to arrange the books but I will not use any one of them to arrange my shelves because I am the laziest person on Earth .

140636779 130636799 130636800 140636800

Utsav Singhal by Utsav Singhal , 22, India

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3 solutions

Baby Googa
Feb 11, 2015

There are 10! ways of arranging the 10 books in a line. There are then 36 (9 choose 2) ways of splitting them into 3 groups. 36*10!=130636800

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Timmy Ben
Feb 11, 2015

This solution for this is 36 * 10!

Consider there every shelf must have at least one book, and there is shelf A, B, C: (A,B,C) = (8,1,1) , (7,2,1), (7,1,2) , (6,3,1), (6,2,2) , (6,1,3)..... and there is 36 combinations.

Since there is 10 different books, so it is 36 * 10P10 = 36 * 10!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Pranjal Jain
Nov 29, 2014

Only one option is perfectly divisible by 10 ! 10! . So no need to solve!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Could give a solid method of solving, please?

Anandhu Raj - 6 years, 5 months ago

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