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Question: How do you calculate the number of combinations for a given total number of objects (n) and a number of objects chosen at one time (x)?

You can calculate the number of combinations using the formula for combinations in mathematics, which is also known as the binomial coefficient. This formula is: C(n, x) = n! / [x!(n-x)!] Here, "n" is the total number of objects, and "x" is the number of objects chosen at a time. "C(n, x)" is the number of combinations. The exclamation point signifies factorial, which means to multiply a series of descending natural numbers. To expand on what factorial means, "n!" denotes the product of all positive integers up to n. For example, 4! = 4*3*2*1 = 24. So, in order to calculate the number of combinations, you first calculate the factorials of n, x, and (n-x), and then plug those values into the formula. It's worth mentioning that in this context, combinations are sets where order doesn't matter. If the order does matter, then you are dealing with permutations, not combinations.

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