SOLUTION: The reading list for a literature class has 7 fiction and 9 nonfiction books. A student is to write a report on 5 books from the list during the semester. The reports must include
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-> SOLUTION: The reading list for a literature class has 7 fiction and 9 nonfiction books. A student is to write a report on 5 books from the list during the semester. The reports must include
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Question 1116838: The reading list for a literature class has 7 fiction and 9 nonfiction books. A student is to write a report on 5 books from the list during the semester. The reports must include at least 1 and at most 4 reports of fiction books. In how many ways can the selection of books be made? Answer by ikleyn(52778) (Show Source):
All possible opportunities are listed in the table below (two most-left columns)
#of fiction books #of non-fiction books #of combinations value
----------------------------------------------------------------------------
1 4 882
2 3 1764
3 2 1260
4 1 315
The third column contains the formulas for the number of selections.
The fourth column contains the values calculated with these formulas:
= = 882;
= = 1764;
= = 1260;
= = 315.
Now your last step is to add all four numbers in the right column: 882 + 1764 + 1260 + 315 = 4221.
Answer. The selection of books can be made in 4221 ways.
