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?
There are 24C12 = 24!/[12!*12!] = 2,704,156 combinations.
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.
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
There are millions of combinations of numbers with a difference of 9. 9 and 0, 10 and 1, 11 and 2, 12 and 3, and so on. The difference is the answer that you get when you subtract two numbers, so any numbers that subtract to an answer of 9 will work.
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 24C12 = 24!/[12!*12!] = 2,704,156 combinations.
30
There are 24C12 = 24*23*...*13/(12*11*...*1) = 2,704,156 combinations.
26 = 64 combinations, including the null combination - which contains no numbers.
Only three: 12, 13 and 23. Remember that the combinations 12 and 21 are the same.
There are 14C5 = 14*13*12*11*10/(5*4*3*2*1) = 2002
The number of combinations of 12 numbers taken 12 at a time (i.e., choosing all 12 numbers from a set of 12) is calculated using the binomial coefficient formula, which is ( \binom{n}{k} = \frac{n!}{k!(n-k)!} ). For ( n = 12 ) and ( k = 12 ), this simplifies to ( \binom{12}{12} = 1 ). Therefore, there is only one combination of 12 numbers from 1 to 12, which includes all the numbers themselves.
To calculate the number of 4-digit combinations you can get from the numbers 1, 2, 2, and 6, we need to consider that the number 2 is repeated. Therefore, the total number of combinations is calculated using the formula for permutations of a multiset, which is 4! / (2!1!1!) = 12. So, there are 12 unique 4-digit combinations that can be formed from the numbers 1, 2, 2, and 6.
11
This question does not make sense since a combination is independent of the order of its elements. That is, the combinations 1245 and 5142 are the same. Consequently, there can be no "last " numbers in a combination.
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.
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