SOLUTION: In how many ways can 5 red, 3 blue, and 2 yellow books be arranged on a shelf with no restrictions? In how many distinguishable ways can 5 red, 3 blue, and 2 yellow books if books

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Question 1032424: In how many ways can 5 red, 3 blue, and 2 yellow books be arranged on a shelf with no restrictions? In how many distinguishable ways can 5 red, 3 blue, and 2 yellow books if books of the same color are identical?
Answer by ikleyn(52781) About Me  (Show Source):
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In how many ways can 5 red, 3 blue, and 2 yellow books be arranged on a shelf with no restrictions?
In how many distinguishable ways can 5 red, 3 blue, and 2 yellow books highlight%28can_be_arranged%29 if books of the same color are identical?
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1.  In how many ways can 5 red, 3 blue, and 2 yellow books be arranged on a shelf with no restrictions? 

    (5 + 3 + 2)! = 10! = 3628800 ways.


2.  In how many distinguishable ways can 5 red, 3 blue, and 2 yellow books can be arranged if books of the same color are identical?

    %285%2B3%2B2%29%21%2F%285%21%2A3%21%2A2%21%29 = %2810%2A9%2A8%2A7%2A6%29%2F%28%281%2A2%2A3%29%2A%281%2A2%29%29 = 10*9*4*7 = 2520 ways.