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Permutation Calculators
Overview:
Permutations the different ways in which a set of items can be arranged or ordered, are a fundamental concept in combinatorics. Each unique arrangement is called a permutation, and understanding this concept is key to mastering the branch of mathematics dealing with combinations and arrangements of objects. When calculating permutations, the order of the items matters. For example, given three letters, A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Each arrangement is distinct from the others, demonstrating how the sequence of items changes the permutation. The number of permutations of a set of nnn distinct items is given by n!n!n! (n factorial), which is the product of all positive integers up to nnn. For instance, for three items (A, B, C), the number of permutations is 3!=3×2×1=6.
Permutations are widely used in probability theory, cryptography, and statistical mechanics. They help solve problems related to arrangement and order, making them essential for understanding patterns and structures in various scientific and practical applications.
Calculator for Permutations With Value Repetition
Description:
Calculate how many different permutations are possible when you have n (number of things to choose from) and r (number of things chosen). Value repetition means same possible thing from n can be chosen more than once for r. Note with permutations order does matter e.g. 123 is not same as 321 and counts as two permutations.
Instructions:
- Enter value for n (number of things to choose from) and r (number of things chosen) in available fields.
- Press solve button to find remaining unknown value.
- To perform a new calculation or you wish to clear current values use the reset button
to clear values and start again. - The formulas used for each calculator can be viewed by expanding the 'Click to Show Formula' section below.
is equal to
requirements not met -
please add all values in available fields.
Click to Show Formula
How many permutations would need to guarantee opening a padlock which has three numbers, each with a possible value to choose between 0 to 9?
Answer:
n (number of things to choose from) = 10
r (number of things chosen) = 3
10 3 = 1000
That's 1000 possible permutations needed to guarantee opening the padlock!
Calculator for Permutations Without Value Repetition
Description:
Calculate how many different permutations are possible when you have n (number of things to choose from) and r (number of things chosen). No value repetition means same possible thing from n can't be chosen more than once for r. Note with permutations order does matter e.g. 123 is not same as 321 and counts as two permutations.
Instructions:
- Enter value for n (number of things to choose from) and r (number of things chosen) in available fields.
- Press solve button to find remaining unknown value.
- To perform a new calculation or you wish to clear current values use the reset button to clear values and start again.
- The formulas used for each calculator can be viewed by expanding the 'Click to Show Formula' section below.
!
(n -
)!
is equal to
requirements not met -
please add all values in available fields.
Click to Show Formula
How many permutations would need to guess a correct password which is 6 letters long, each letter must be from the alphabet , can only be used once and is none case sensitive e.g. `a` is same as `A`?
Answer:
n (number of things to choose from) = 26
r (number of things chosen) = 6
26! ÷ (26 - 6)! = 165,765,600
That`s 165,765,600 possible permutations needed to guarantee guessing the correct password!