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Combination Calculators
Overview:
Combinations a straightforward mathematical concept, are used to determine the number of ways a subset of items can be selected from a larger set, where the order of selection does not matter. This simplicity sets them apart from permutations, where order is important. Combinations focus solely on the selection of items, not their arrangement, making them easy to grasp and apply.
For example, if you have a set of 5 fruits (apple, banana, cherry, date, and elderberry) and want to select 3 of them, the number of possible combinations is 10. These combinations include sets like {apple, banana, cherry}, {apple, banana, date}, and so on.
Combinations are used in various fields, such as statistics, probability, and optimization, where the focus is on selecting groups or subsets from a larger pool of items without concern for order. They help analyze situations where the arrangement of items is irrelevant, making them valuable for solving problems related to grouping and selection.
Calculator for Combinations With Value Repetition
Description:
Calculate how many different combinations are possible when you have n (number of things to choose from) and r (number of things chosen). Repetition means same possible thing from n can be chosen more than once for r. Note with combinations order does not matter e.g. 123 is same as 321 and counts as one combination.
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.
(r +
- 1)!
(n -
)! r!
is equal to
requirements not met -
please add all values in available fields.
Calculation History
Note: only shows calculations performed in current session - If you refresh the page all history will be removed.
Click to Show Formula
Calculator for Combinations Without Value Repetition
Description:
Calculate how many different combinations are possible when you have n (number of things to choose from) and r (number of things chosen). No repetition means same possible thing from n can`t be chosen more than once for r. Note with combinations order does not matter e.g. 123 is same as 321 and counts as one combination.
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 -
)! r!
is equal to
requirements not met -
please add all values in available fields.
Calculation History
Note: only shows calculations performed in current session - If you refresh the page all history will be removed.
Click to Show Formula
How many lottery tickets would you need to purchase to guarantee a win if there are 6 numbers on a ticket each with a possible value of 1 to 59 and each number can only be chosen once? (note : order of numbers chosen does not need to match order that numbers are drawn only values of numbers chosen vs. drawn need to match.)
Answer:
n (number of things to choose from) = 59
r (number of things chosen) = 6
59! ÷ ((59 - 6)! x 6!) = 45,057,474
That`s 45,057,474 possible combinations!