How to Take 24 Numbers & Calculate All Combinations

Combinations allow you to calculate how many different ways you can arrange 24 numbers.
••• Jupiterimages/Comstock/Getty Images

The possible ways to combine 24 numbers depend on whether their order matters. If it does not, you need to simply calculate a combination. If the order of the items does matter, then you have an ordered combination called a permutation. One example would be a 24-letter password where the order is crucial. When performing the calculation, you need to know if you will have repetition. Repetition means you can select any number, and the number is available to select again. Without repetition, you can select the number only once.

    Raise 24 to the 24th power to calculate the number of combinations you can have with repetition, that is, using a number more than once. For example, you have 24 playing cards and each time a card is picked, it goes back into the deck and is available to pick again. Raising a number to a power is another way to say you are using exponents, multiplying 24 by itself 24 times. So, 24 raised to the 24th power is 1,333,735,776,850,280,000,000,000,000,000,000. This is how many combinations are possible if you can pick any of the 24 numbers more than once.

    Write out the formula in order to calculate the number of combinations without repetition. So, with the 24 playing cards, after a card is dealt, you do not put it back into the deck. The formula starts with 24, then you multiply that by 23, then by 22 and so forth. So your formula will look like this: 24x23x22x21x20x19x18... all the way to 1.

    Solve your formula. In this example, the equation equals 620,448,401,733,239,000,000,000, the number of possible combinations if numbers are not available to pick more than once.

Related Articles

How to Calculate Combinations & Permutations
How to Factor Monomials
Definition of Successor and Predecessor in Math
How to Know if a Number is Divisible by 9
How to Solve Operations Puzzles
What Is Math Regrouping?
How to Round Numbers in Money
How to Calculate Combinations & Permutations
How to Calculate Interest Rates
How to Write Math Arrays
How to Save Notes on a TI-83 Plus
How to Find Linear Functions
How to Find All The Factors of a Number Quickly and...
Definition of Mean, Median & Mode
How to Calculate a Coprime
How to Write an Improper Fraction As a Whole Number
How to Write a Repeating Decimal As a Fraction
How to Find Fraction Sequences
How to Solve for Range

Dont Go!

We Have More Great Sciencing Articles!