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!)
There are 15 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.
Number of 7 digit combinations out of the 10 one-digit numbers = 120.
9999
You can make 5 combinations of 1 number, 10 combinations of 2 numbers, 10 combinations of 3 numbers, 5 combinations of 4 numbers, and 1 combinations of 5 number. 31 in all.
120 WRONG! That is the number of PERMUTATIONS. In the case of combinations, the order of the numbers does not matter, so there is only 1 5-number combination from 5 numbers.
If you can repeat the numbers within the combination there are 10,000 different combinations. If you cannot repeat the numbers within the combination, there are 5040 different combinations.
all numbers have to be different 720 360 (6*5*4*3*2*1), * * * * * Wrong. Combinations do not have to be different. Those are permutations. There are only 6C4 = 6*5/(2*1) = 15 combinations.
7
There are 15 combinations.
-- 4 numbers can be lined up in 24 different ways-- If the order doesn't matter, then there's only one4-number combination of 4 numbers.
There are 360 of them.
If the numbers can be repeated and the numbers are 0-9 then there are 1000 different combinations.
14 * * * * * Wrong! There are 15. 4 combinations of 1 number, 6 combinations of 2 number, 4 combinations of 3 numbers, and 1 combination of 4 numbers.
There is only one five-number combination of 5 distinct numbers.
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.
There are different numbers of combinations for groups of different sizes out of 9: 1 combination of 9 digits 9 combinations of 1 digit and of 8 digits 36 combinations of 2 digits and of 7 digits 84 combinations of 3 digits and of 6 digits 126 combinations of 4 digits and of 5 digits 255 combinations in all.