Calculator Use
Like the Combinations Calculator the Permutations Calculator finds the number of subsets that can be taken from a larger set. However, the order of the subset matters. The Permutations Calculator finds the number of subsets that can be created including subsets of the same items in different orders.
- Factorial
- There are n! ways of arranging n distinct objects into an ordered sequence, permutations where n = r.
- Combination
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
- Permutation
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed. When n = r this reduces to n!, a simple factorial of n.
- Combination Replacement
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are allowed.
- Permutation Replacement
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are allowed.
- n
- the set or population
- r
- subset of n or sample set
Permutations Formula:
Therefore the number of permutations of 4 different things is. Thus the number of permutations of 4 different things taken 4 at a time is 4! (See Topic 19.) (To say 'taken 4 at a time' is a convention. Is the number of permutations of 4 different things taken from a total of 4 different things.' Permute definition: to change the sequence of Meaning, pronunciation, translations and examples.
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( P(n,r) = dfrac{n!}{(n - r)! } )
For n ≥ r ≥ 0.
Calculate the permutations for P(n,r) = n! / (n - r)!. 'The number of ways of obtaining an ordered subset of r elements from a set of n elements.'[1] Secret world of alex mac cat.
Permutation Problem 1
Choose 3 horses from group of 4 horses
In a race of 15 horses you beleive that you know the best 4 horses and that 3 of them will finish in the top spots: win, place and show (1st, 2nd and 3rd). So out of that set of 4 horses you want to pick the subset of 3 winners and the order in which they finish. How many different permutations are there for the top 3 from the 4 best horses?
For this problem we are looking for an ordered subset of 3 horses (r) from the set of 4 best horses (n). We are ignoring the other 11 horses in this race of 15 because they do not apply to our problem. We must calculate P(4,3) in order to find the total number of possible outcomes for the top 3 winners.
P(4,3) = 4! / (4 - 3)! = 24 Possible Race Results
If our 4 top horses have the numbers 1, 2, 3 and 4 our 24 potential permutations for the winning 3 are {1,2,3}, {1,3,2}, {1,2,4}, {1,4,2}, {1,3,4}, {1,4,3}, {2,1,3}, {2,3,1}, {2,1,4}, {2,4,1}, {2,3,4}, {2,4,3}, {3,1,2}, {3,2,1}, {3,1,4}, {3,4,1}, {3,2,4}, {3,4,2}, {4,1,2}, {4,2,1}, {4,1,3}, {4,3,1}, {4,2,3}, {4,3,2}
Permutation Problem 2
Choose 3 contestants from group of 12 contestants
At a high school track meet the 400 meter race has 12 contestants. The top 3 will receive points for their team. How many different permutations are there for the top 3 from the 12 contestants?
For this problem we are looking for an ordered subset 3 contestants (r) from the 12 contestants (n). We must calculate P(12,3) in order to find the total number of possible outcomes for the top 3.
P(12,3) = 12! / (12-3)! = 1,320 Possible Outcomes
Permutation Problem 3
Choose 5 players from a set of 10 players
An NFL team has the 6th pick in the draft, meaning there are 5 other teams drafting before them. If the team believes that there are only 10 players that have a chance of being chosen in the top 5, how many different orders could the top 5 be chosen?
Plugin manager mac. For this problem we are finding an ordered subset of 5 players (r) from the set of 10 players (n).
P(10,5)=10!/(10-5)!= 30,240 Possible Orders
References
[1] For more information on permutations and combinations please see Wolfram MathWorld: Permutation.
Rearrange dimensions of multidimensional array dimensions
Description
The Permute Dimensions block reorders the elements of the input signal by permuting its dimensions. You specify the permutation to be applied to the input signal using the Order parameter.
For example, to transpose a 3-by-5 input signal, specify the permutation vector
[2 1]
for the Order parameter. When you do, the block reorders the elements of the input signal and outputs a 3-by-5 matrix.You can use an array of buses as an input signal to a Permute Dimensions block. For details about defining and using an array of buses, see Combine Buses into an Array of Buses.
Input
Port_1
— Input signal
scalar | vector | matrix | N-D array
This port accepts scalar, vector, matrix, and N-dimensional signals of any data type that Simulink® supports, including fixed-point, enumerated, and nonvirtual bus data types.
Data Types:
half
| single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| Boolean
| fixed point
| enumerated
| bus
Output
Port_2
— Permutation of input signal
scalar | vector | matrix | N-D array
The block outputs the permutation of the input signal, according to the value of the Order parameter. The output has the same data type as the input.
Data Types:
half
| single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| Boolean
| fixed point
| enumerated
| bus
Parameters
Order
— Permutation vector
[2,1]
(default) | N
-element vector, where N
is the number of dimensions of the input signal
Specify the permutation order to apply to the dimensions of the input signal. The value of this parameter must be an
N
-element vector where N
is the number of dimensions of the input signal. The elements of the permutation vector must be a rearrangement of the values from 1 to N
.For example, the permutation vector
[2 1]
applied to a 5-by-3 input signal results in a 3-by-5 output signal, in other words, the transpose of the input signal.Programmatic Use
Block Parameter: Order |
Type: character vector |
Value: N-element vector |
Default: '[2 1]' |
Model Examples
Use the Permute Dimensions block to permute the first and third dimensions of a 3-by-4-by-5 input array.
Block Characteristics
2+2=4 Is Racist
Data Types | Boolean | bus | double | enumerated | fixed point | half | integer | single |
Direct Feedthrough | yes |
Multidimensional Signals | no |
Variable-Size Signals | yes |
Zero-Crossing Detection | no |
Extended Capabilities
Permute 2 2 4 4 Tetramethylpentane
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.
See Also
Permute 2 2 4 4 Tetraethylbicyclo 1 1 0 Butane
Math Function |
permute
Topics
Introduced in R2007a