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## Permutation using the calculator Casio fx-991ES

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## How do you calculate permutations without repetition?

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**To calculate the number of permutations - nPr:**

- Determine how many numbers you want to choose from the original set. Assume its 4.
- Use the permutation without repetition formula: nPr= n!/(n - r)! …
- Solve the equation: nPr = 11!/(11 - 4!) = 11!/7! …
- The number of permutations equals 7920.

How do you find the number of permutations without repetition?

**To calculate the number of permutations - nPr:**

- Determine how many numbers you want to choose from the original set. Assume its 4.
- Use the permutation without repetition formula: nPr= n!/(n - r)! …
- Solve the equation: nPr = 11!/(11 - 4!) = 11!/7! …
- The number of permutations equals 7920.

How many combinations of 4 items have no repeats?

Answer and Explanation: The number of possible combinations with 4 numbers without repetition is 15. The formula we use to calculate the number of n element combinations when repetition is not allowed is **2n - 1**.

How do you do permutations without replacement?

Without replacement means **the same item cannot be selected more than once**. 10 X 10 X 10 X 10 = 10,000 combinations are possible. The PIN code is an example when order is important. The PIN code 1234 is different from the PIN code 4321.

## How do you write a permutation as a product of cycles?

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A permutation with cycle type ( a 1 , a 2 , … , a n ) can be written as a product of **a 2 + 2 a 3 + ⋯ + ( n - 1 ) a n = n - ( a 1 + a 2 + ⋯ + a n ) transpositions, and no fewer**. For the example (26.13. 2), this decomposition is given by ( 1 , 3 , 2 , 5 , 7 ) ( 6 , 8 ) = ( 1 , 3 )

How do you write a permutation in cycle form?

A permutation with cycle type ( a 1 , a 2 , … , a n ) can be written as **a product of a 2 + 2 a 3 + ⋯ + ( n - 1 ) a n = n - ( a 1 + a 2 + ⋯ + a n ) transpositions, and no fewer**. For the example (26.13. 2), this decomposition is given by ( 1 , 3 , 2 , 5 , 7 ) ( 6 , 8 ) = ( 1 , 3 )

Can a permutation be written as a product of 3 cycles?

Thus **any pair of transpositions can be written as a product of 3-cycles**, so the permutation σ can be written as the product of 3-cycles as well.

How do you find the product of permutations?

To calculate the number of permutations, **take the number of possibilities for each event and then multiply that number by itself X times, where X equals the number of events in the sequence**.

## How do you calculate permutations with repetition?

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…

Formulas for Permutations.

Formulas to Calculate Permutation | |
---|---|

Permuation Formula | ^{n}P_{r} = n! / (n−r)! |

Permutation with Repetition Formula | ^{n}P_{r} = n^{r} |

Can you have repetition in permutations?

Permutations: order matters, **repetitions are not allowed**. (regular) Combinations: order does NOT matter, repetitions are not allowed. Combinations WITH Repetitions: order does NOT matter, repetitions ARE allowed.

What is the formula for calculating permutations?

One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: **P(n,r)=n!** **(n−r)!**

How many ways can you arrange 4 letters with repetition?

The answer is 4! = **24**. The first space can be filled by any one of the four letters. The second space can be filled by any of the remaining 3 letters.

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