Math Problem Statement
8 fiction novels by new authors are on display at a Book Festival.Patrons are told that they can choose any 3 books. How many different selections can a patron make?
Solution
This problem can be solved using combinations since the order in which the books are selected doesn't matter. The formula for combinations is given by:
Where:
- is the total number of items (in this case, books),
- is the number of items to be chosen.
Here:
- (total books),
- (books to be selected).
Substituting these values into the combination formula:
Simplifying the factorials:
So, the number of different selections a patron can make is 56.
Would you like any further details or explanations?
Here are 5 related questions to think about:
- How would the solution change if the patron could only choose 2 books instead of 3?
- What if there were 10 books to choose from instead of 8?
- How many selections could a patron make if they were allowed to choose up to 4 books?
- What if the patron could select the same book more than once (allowing repetitions)?
- How would this change if the order of selection mattered (permutations)?
Tip: Remember that combinations are used when the order of selection doesn't matter, while permutations are used when order does matter.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Combinations
Formulas
C(n, r) = n! / (r!(n - r)!)
Theorems
Combinatorial Selection Theorem
Suitable Grade Level
Grades 9-12