Permutation, Combination, and Counting Principal

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•
Mathematics
•
9th - 11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a permutation?
Back
A permutation is an arrangement of objects in a specific order. The order matters in permutations.
2.
FLASHCARD QUESTION
Front
What is a combination?
Back
A combination is a selection of objects where the order does not matter. It focuses on the group rather than the arrangement.
3.
FLASHCARD QUESTION
Front
How do you calculate the number of permutations of n objects taken r at a time?
Back
The formula is P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.
4.
FLASHCARD QUESTION
Front
How do you calculate the number of combinations of n objects taken r at a time?
Back
The formula is C(n, r) = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects to choose.
5.
FLASHCARD QUESTION
Front
What is the counting principle?
Back
The counting principle states that if one event can occur in m ways and a second can occur independently in n ways, then the two events can occur in m * n ways.
6.
FLASHCARD QUESTION
Front
Example of a permutation: Arranging 3 books on a shelf. How many ways can this be done?
Back
There are 6 ways to arrange 3 books (3! = 6).
7.
FLASHCARD QUESTION
Front
Example of a combination: Choosing 2 fruits from a basket of 5. How many combinations are possible?
Back
There are 10 combinations (C(5, 2) = 5! / (2! * 3!) = 10).
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