SOLUTION: Ten different books are to be arranged on a shelf. Two of the books are by E. Smith, three of the books are by A. Houseman and the remaining books are all by different authors. How

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Question 307809: Ten different books are to be arranged on a shelf. Two of the books are by E. Smith, three of the books are by A. Houseman and the remaining books are all by different authors. How many ways can the books be arranged on the shelf if Smith's books and Houseman's books must be kept together?

So far what I have is (2!)(3!)(5!) Not sure if thats right or not. My answer was 1440.
Any help will be much appreciated. :)
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
you have Smith, Houseman, and five other books ___ 7 things

order counts, so 7!

BUT (yeah, there's always one) the Smith and Houseman groups have their own arrangements within the groups

so ___ (7!)(2!)(3!)

looks like you had the sub-groups okay