SOLUTION: Any help would be so appreciated. Thank you. 10 books are to be arranged on a shelf. 4 of the books have red covers, 3 have green covers, and another 3 have gray covers. In how

Question 488859: Any help would be so appreciated. Thank you.
10 books are to be arranged on a shelf. 4 of the books have red covers, 3 have green covers, and another 3 have gray covers. In how many ways can the books be arranged on a shelf if books of the same color must be arranged together?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Without ordering the books of the same color,
here is the possible ways to order books of different colors:
(1) [ 4 red ][ 3 green ][ 3 gray ]
(2) [ 4 red ][ 3 gray ][ 3 green ]
----------------------
(3) [ 3 green ][ 4 red ][ 3 gray ]
(4) [ 3 gray ][ 4 red ][ 3 green ]
----------------------
(5) [ 3 gray ][ 3 green ][ 4 red ]
(6) [ 3 green ][ 3 gray ][ 4 red ]
----------------------
So, there are 6 different ways to order
books of different colors (1) through (6)
The possible ways that books of the same color
can be ordered for each of the (6) is:

----------------------
You can have (1) OR (2) OR (3) OR (4) OR (5) OR (6)
So, the choices for different color orderings get added

There are 5184 possible arrangements of the books
You should get other opinions, too.

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