In math, the term permutation is the process of rearranging the given number of elements or objects. For example set {a,b,c), namely [a,b,c], [a,c,b], [b,a,c], [b,c,a], [c,a,b], and [c,b,a].
Formula for finding permutation: P(n,r) = `(n!) / ((n-r)!)` , where, n gives number of things, and r gives number of times.
Using permutation we can find how many possible ways are there to arrange the collection of objects. Permutation avoids the repletion. In this article we will discuss about the math term permutation and how to find the permutation.
Math Term Permutation – Example Problems
Example 1: How many different ways can a set of five country flags are arranged?
Solution:
P(5,5) = `(5!)/((5 - 5)!)` = `(5 * 4 * 3 * 2 * 1!) / (0!)` = 120 [0! = 1]
Therefore 120 possible ways are there to arrange a five flags.
Example 2: In how many ways 5 chocolates can be chosen from among 9 different kinds of chocolates?
Solution:
This problem involves 10 candies, taken 5 at a time.
P(10,5) = `(10!) / ((10 - 5)!)` = `(10 * 9 * 8 * 7 * 6 * 5!) / (5!)` = 30240
There are 30240 possible ways to choose 5 chocolates among 10 chocolates.
Example 3: Peter bought four movies. In how many different ways can he watch the four movies?
Solution:
P(4,4) = `(4!) / ((4 - 4)!)` = `(4 * 3 * 2 * 1) / (0!)` = 24 [0! = 1]
In 24 different ways he can watch the four movies.
Example 4: The computer password has 4 digits, if the possible digits are 2, 4, 5, 6, 7, 8, 9. How many different passwords can be made?
Solution:
This problem involves 7 digits, 4 digits at a time.
P(7,4) = `(7!) / ((7 - 4)!)` = `(7 * 6 * 5 * 4 * 3!) / (3!)` = 840
Therefore, 840 different passwords can be made.
Math Term Permutation – Practice Problems
Problem 1: How many different ways can a set of seven country flags are arranged?
Problem 2: In how many ways can 6 candies chosen from among 9 different colors of candies?
Problem 3: Anita bought six movies. In how many different ways can she watch the six movies?
Answer: 1) 5040 2) 60480 3) 720
Formula for finding permutation: P(n,r) = `(n!) / ((n-r)!)` , where, n gives number of things, and r gives number of times.
Using permutation we can find how many possible ways are there to arrange the collection of objects. Permutation avoids the repletion. In this article we will discuss about the math term permutation and how to find the permutation.
Math Term Permutation – Example Problems
Example 1: How many different ways can a set of five country flags are arranged?
Solution:
P(5,5) = `(5!)/((5 - 5)!)` = `(5 * 4 * 3 * 2 * 1!) / (0!)` = 120 [0! = 1]
Therefore 120 possible ways are there to arrange a five flags.
Example 2: In how many ways 5 chocolates can be chosen from among 9 different kinds of chocolates?
Solution:
This problem involves 10 candies, taken 5 at a time.
P(10,5) = `(10!) / ((10 - 5)!)` = `(10 * 9 * 8 * 7 * 6 * 5!) / (5!)` = 30240
There are 30240 possible ways to choose 5 chocolates among 10 chocolates.
Example 3: Peter bought four movies. In how many different ways can he watch the four movies?
Solution:
P(4,4) = `(4!) / ((4 - 4)!)` = `(4 * 3 * 2 * 1) / (0!)` = 24 [0! = 1]
In 24 different ways he can watch the four movies.
Example 4: The computer password has 4 digits, if the possible digits are 2, 4, 5, 6, 7, 8, 9. How many different passwords can be made?
Solution:
This problem involves 7 digits, 4 digits at a time.
P(7,4) = `(7!) / ((7 - 4)!)` = `(7 * 6 * 5 * 4 * 3!) / (3!)` = 840
Therefore, 840 different passwords can be made.
Math Term Permutation – Practice Problems
Problem 1: How many different ways can a set of seven country flags are arranged?
Problem 2: In how many ways can 6 candies chosen from among 9 different colors of candies?
Problem 3: Anita bought six movies. In how many different ways can she watch the six movies?
Answer: 1) 5040 2) 60480 3) 720
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