The answer is 15C6 = 15*14*13*12*11*10/(6*5*4*3*2*1) = 5,005
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10 * * * * * That is just plain wrong! It depends on how many numbers in each combination but there are 1 combination of 4 numbers out of 4, 4 combinations of 3 numbers out of 4, 6 combinations of 2 numbers out of 4, 4 combinations of 1 number out of 4. A grand total of 15 (= 24-1) combinations.
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To calculate the number of 4-number combinations possible with 16 numbers, you would use the formula for combinations, which is nCr = n! / r!(n-r)!. In this case, n = 16 (the total number of numbers) and r = 4 (the number of numbers in each combination). Plugging these values into the formula, you would calculate 16C4 = 16! / 4!(16-4)! = 1820. Therefore, there are 1820 possible 4-number combinations with 16 numbers.
6C4 = 6*5/(2*1) = 15
It depends on whether the order of the numbers is important or not. For example, if 123456 is seen as a different code to 213456 then there are many more possible solutions.If the order is unimportant, the number of possible combinations is equal tobinomial coefficient(15,6) = 5005If the order is important, then the number of possible permutations is equal to15! = ~1.3x1012