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.
About the Author
Carter McBride started writing in 2007 with CMBA's IP section. He has written for Bureau of National Affairs, Inc and various websites. He received a CALI Award for The Actual Impact of MasterCard's Initial Public Offering in 2008. McBride is an attorney with a Juris Doctor from Case Western Reserve University and a Master of Science in accounting from the University of Connecticut.