10C2

The mathematical expression 10C2 represents a combination, specifically the number of ways to choose 2 items from a set of 10 distinct items, where the order of selection does not matter. This is part of combinatorics, a branch of mathematics concerned with counting, arrangement, and combination of objects. The formula for combinations is generally expressed as nCr = n! / (r! (n-r)!), where n is the total number of items, and r is the number of items to choose. In this case, n=10 and r=2.

Applying the formula, 10C2 = 10! / (2! (10-2)!). This expands to 10! / (2! 8!). The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. So, 10! = 10 9 8 7 6 5 4 3 2 1, 2! = 2 1, and 8! = 8 7 6 5 4 3 2 1.

Calculating the values, 10! = 3,628,800, 2! = 2, and 8! = 40,320. Substituting these into the formula: 10C2 = 3,628,800 / (2 40,320). This simplifies to 3,628,800 / 80,640. The result of this division is 45. Therefore, there are 45 distinct ways to choose 2 items from a set of 10 items when the order of selection is not considered. This calculation is frequently used in probability and statistics to determine the number of possible outcomes in various scenarios.