Pascal's Triangle & Combinations Exploration

[size=150]To generate Pascal's triangle, you start with a row containing only the number 1. Each subsequent row is formed by adding adjacent numbers from the row above, and each row starts and ends with 1.[br]Here is an example of Pascal's triangle with 6 rows:[br][br]1[br]1 1[br]1 2 1[br]1 3 3 1[br]1 4 6 4 1[br]1 5 10 10 5 1[br][br]To calculate combinations, you can use the formula: nCk = n! / (k! * (n - k)!), where n is the total number of items and k is the number of items being chosen. The exclamation mark (!) denotes the factorial of a number, which is the product of all positive integers up to that number.[br][br]For example, let's calculate "5 choose 2" (5C2):[br]nCk = 5! / (2! * (5 - 2)!)[br][br]Calculating the factorials:[br]5! = 5 * 4 * 3 * 2 * 1 = 120[br]2! = 2 * 1 = 2[br](5 - 2)! = 3! = 3 * 2 * 1 = 6[br][br]Plugging in the values:[br]5C2 = 120 / (2 * 6)[br] = 120 / 12[br] = 10[br]So, "5 choose 2" is equal to 10.[br][br]By following this process, you can generate Pascal's triangle and calculate combinations without writing any code.[/size]
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