How many combinations are there for 1 thru 4?

Question

From a statistics course 40 years ago I thought 16. I listed them and came up with 24. What the? Perhaps the correct term is permutations.

I think I mess up the question, I should not use permutations and combinations in the same question. I see how 24 is computed. Thanks for answers.

Answer 1

just multiply 4*3*2*1, a permutation also known as 4!

Answer 2

If you do mean permutation, a listing of 1 through 4 in some order, then you have 4 options for the first term, 3 options for the second, 2 for the third, and one for the fourth. this yields 4*3*2*1 or 24 choices, as those above have mentioned.

This can be extended to finding the number of permutations of N numbers, by doing N!.

If you do mean combination, then you need to find all the ways to pick 4 (1), pick 3 (4, the same as picking one to not choose), pick 2(6), pick 1 (4) AND pick 0 (1). This will yield a total of 16 different combinations.

In general, for a given set of N numbers, you can pick 2^N subsets. Each number can be either in or out of the subset, and you have to repeat this N times.

Answer 3

Yup, 24. the answer is 4!=4*3*2*1=24

Answer 4

the answer is 4 times 3 times 2 times 1 which is 24, you were right :)

Answer 5

Since you know there are 4 numbers you take 4! Which also means 4x3x2x1 which equals 24

Answer 6

It depends on how many numbers you want to combine from 1 through 4. If there is no specific instruction as to how many numbers you need to combine then that means you need to count all combinations possible with only 1 number, 2 numbers, 3 number and 4 numbers.

the general formula for combinations is n! / (n-k)!(n!)
where k is the specific number of objects you want to combine;
where n is the total number of objects you can choose from.
this formula counts repeated combinations as 1 count.
for example if you combine only 2 numbers from 1 through 4, you get:
1,2 and 2,1 are counted as 1 count NOT as 2 counts
1,3 and 3,1 are counted as 1 count
1,4 and 4,1 are counted as 1 count
2,2 is not counted because there is only one '2' from 1 through 4
2,3 and 3,2 are counted as 1 count
2,4 and 4,2 are counted as 1 count
3,3 is not counted
3,4 and 4,3 are counted as 1 count
4,4 is not counted
So there are 6 possible combinations when you take 2 numbers at a time from 1 through 4

Solving your problem...
Combination for only 1 number from 1 through 4:
= 4! / (4-1)!(1!) = 4!/3! = 4

Combination for only 2 numbers from 1 through 4:
= 4! / (4-2)!(2!) = 4!/2! = 4x3x2! / 4 = 6

Combination for only 3 numbers from 1 through 4:
= 4! / (4-3)!(3!) = 4!/(1!)(3!) = 4x3!/3! = 4

Combination for all 4 numbers from 1 through 4:
= 4! / (4-4)!(4!) = 4!/4! = 1

Total number of combinations is thus 4+6+4+1 = 15

Answer 7

16 is correct. 4 x 4 =16.

Answer 8

4!= 4x3x2x1=24

Answer 9

you have to do 4! (factorial)
4x 3x 2x 1= 24