Assuming no repetition, 12 x 11 x 10.... x 4 x 3 x 2.
If repetition is allowed, 1212
There are 24C12 = 24!/[12!*12!] = 2,704,156 combinations.
12
There are 24C12 = 24*23*...*13/(12*11*...*1) = 2,704,156 combinations.
12
30
Only three: 12, 13 and 23. Remember that the combinations 12 and 21 are the same.
26 = 64 combinations, including the null combination - which contains no numbers.
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.
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 12-number combinations using numbers 1-36, we can use the formula for combinations: nCr = n! / r!(n-r)!, where n is the total number of items to choose from (36) and r is the number of items to choose (12). Plugging in the values, we get 36C12 = 36! / 12!(36-12)! = 36! / 12!24! = (363534*...25) / (121110...*1). This simplifies to 125,736,770 unique combinations.
11
To find how many ways to make 12 with three single-digit numbers (from 0 to 9), we can consider combinations of numbers that add up to 12. The valid combinations include repetitions of numbers, such as (3, 4, 5) and (2, 5, 5). However, since the order of addition matters, each unique combination can be arranged in multiple ways, which increases the total count. A systematic approach or generating functions can be used to enumerate all valid combinations and permutations, leading to a total of 29 distinct combinations.