SOLUTION: In a box there are: 7 red books, 5 white books, and 6 blue books. Three books are selected. How many different ways can this be done if the selection: (a) must contain one of eac

Algebra.Com
Question 1018796: In a box there are: 7 red books, 5 white books, and 6 blue books. Three books are selected.
How many different ways can this be done if the selection:
(a) must contain one of each color? c(7,1)c(5,1)c(6,1)= 210
(b) must contain all the same color? c(7,3)+c(5,3)+c(6,3)=65
(c) must include more than one color? I'm not sure how to set this up can you please guide me through?
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
(c) must include more than one color? 

There are 7+5+6 = 18 books.
We can choose 3 book any of c(18,3) = 816 ways.

But, from those 816 ways to choose any 3 books, we
must subtract the number of ways they were all
the same color, which you found correctly to be 
65 in part (b).  c(7,3)+c(5,3)+c(6,3)=65

Answer: 816-65 = 751 ways.

Edwin
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
C(18,3) = 816 is the number of ways of selecting any three books from the eighteen books without any restriction.
Now the number of ways in which one book of each color is selected is 210, which you have correctly determined. The complement of this event is the event in which AT LEAST one book of some color is selected.
Thus, the number of ways in which a selection includes more than one color is
816 - 210 = 606.
RELATED QUESTIONS

In how many ways can 5 red books,4 blue books,and 3 white books be arranged in a... (answered by ikleyn)
There are 4 different mathematics books and 5 different science books in how many ways... (answered by ikleyn)
In how many ways can three different math books and four different English books be... (answered by sudhanshu_kmr)
There are 6 Math books, 4 English books and 7 Filipino books on a shelf. How many ways... (answered by ikleyn)
there are 6 math books 4 english books and 7 filipino books on a shelf how many ways can... (answered by ewatrrr)
A bookshelf displays different types of books, 6 books in English (E) and 5 books in... (answered by Solver92311)
There are 15 different books. How many groups of 6 books can be selected? (answered by edjones)
There are 15 different books. How many groups of 6 books can be selected? (answered by ikleyn)
There are 7 books, 3 red, 2 blue, 1 orange. How many ways can these books be arranged on (answered by ikleyn)