There are 24C12 = 24!/[12!*12!] = 2,704,156 combinations.
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Well, honey, since you're picking 12 numbers out of 24, you're looking at a combination situation. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items you're choosing. So, in this case, it would be 24C12 = 24! / (12!(24-12)!). Plug that into a calculator, and you'll get your answer. Math can be a real hoot, can't it?
To calculate the number of combinations with three numbers, you would use the formula for combinations, which is nCr = n! / r!(n-r)!. In this case, n is the total number of numbers you have to choose from, and r is the number of numbers you are choosing. So, if you have three numbers to choose from, there would be 3C3 = 3! / 3!(3-3)! = 6 / (6*0!) = 6 / 6 = 1 combination.
To find the number of combinations to make 40 using the numbers 12 and 4, we can use a mathematical approach. Since we are looking for combinations, not permutations, we need to consider both the order and repetition of the numbers. One way to approach this is by using a recursive formula or dynamic programming to systematically calculate the combinations. Another approach is to use generating functions to represent the problem and then find the coefficient of the term corresponding to 40 in the expansion of the generating function. Both methods require a deep understanding of combinatorics and mathematical algorithms to accurately determine the number of combinations.
There are 12 different combinations of 3 positive odd numbers that add up to 21. Namely: (There are many permutations of these combinations.) 1,1,9 1,3,17 1,5,15 1,7,13 1,9,11 3,3,15 3,5,13 3,7,11 3,9,9 5,5,11 5,7,9 7,7,7
If the sequence is important, then there are (12 x 11 x 10 x 9 x 8) = 95,040 different ones. If only the members of the group are important but not their the sequence, then there are 95,040 / (5 x 4 x 3 x 2 x 1) = 792 combinations, each with different members. The formulas are: Permutations = 12! / 7! Combinations = 12! / (7! x 5!)