Assuming that the only permitted operation is addition, then there are 4 combinations.
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?
You can make 6 combinations with 3 numbers. They are: 123 213 312 132 231 321 * * * * * NO! Those are permutations! In combitorials, the order does not matter so that the combination 123 is the same as the combination 132 etc. So all of the above comprise just 1 combination. With three numbers you can have 1 combination of three numbers (as discussed above), 3 combinations of 2 numbers (12, 13 and 23) 3 combinations of 1 number (1, 2 and 3) In all, with n numbers you can have 2n - 1 combinations. Or, if you allow the null combination (that consisting of no numbers) you have 2n 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!)
You would get 4!/2! = 12 combinations.
There are 24C12 = 24*23*...*13/(12*11*...*1) = 2,704,156 combinations.
There are 12C4 4 NUMBER combinations. And that equals 12*11*10*9/(4/3/2/1) = 495 combinations. However, some of these, although 4 number combinations consist of 7 digits eg 1, 10, 11, and 12. Are you really sure you want 4-DIGIT combinations?
30
Only three: 12, 13 and 23. Remember that the combinations 12 and 21 are the same.
If they can repeat, then: 17^6=24,137,569 If they can't repeat, then: 17*16*15*14*13*12=8,910,720
26 = 64 combinations, including the null combination - which contains no numbers.
Assuming that the only permitted operation is addition, then there are 4 combinations.
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?
1 and 11 and 21 and 31 and 42 and 12 and 22 and 32 and 43 and 13 and 23 and 33 and 44 and 14 and 24 and 34 and 416 combinations
There are 4 numbers between 0 and 3. Had this been a permutation problem, the answer would be 4!/2!=4*3=12, but this is a combinations problem. Since the duplicates (12 vs 21) come in pairs of 2, we divide the permutaions solution by 2!. Since 2! is just 2, 12/2 = 6 combinations in total.
You can make 6 combinations with 3 numbers. They are: 123 213 312 132 231 321 * * * * * NO! Those are permutations! In combitorials, the order does not matter so that the combination 123 is the same as the combination 132 etc. So all of the above comprise just 1 combination. With three numbers you can have 1 combination of three numbers (as discussed above), 3 combinations of 2 numbers (12, 13 and 23) 3 combinations of 1 number (1, 2 and 3) In all, with n numbers you can have 2n - 1 combinations. Or, if you allow the null combination (that consisting of no numbers) you have 2n combinations.