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.
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.
Number of 7 digit combinations out of the 10 one-digit numbers = 120.
There is only one combination. The order does not matter in a combination.
9999
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.