number combinations that can be made using only the numbers 8,6,2,4.

Question

I want a list of all the numbers made from rearranging the numbers 2, 6, 4, 8.

Answer 1

There are 24 possible permutations: 2468, 2486, 2648, 2684, 2846, 2864, 4268, 4286, 4628, 4682, 4826, 4862, 6248, 6284, 6428, 6482, 6824, 6842, 8246, 8264, 8426, 8462, 8624, 8642.

Answer 2

It is a permutation problem. If the number can be used repeatedly, it will become 4 x 4 x 4 x 4 = 256 four digit numbers. If the number only can be used once, then the answer is 4 x 3 x 2 x 1 = 24 four digit numbers.

Solved Examples of  Permutations

Answer 3

We are listing all 4-figure numbers consist of 4 digits,8,6,4,2, and arranged in different orders.

First, we'll have 4 choises. Take "8", for example, and place it at the head of 4-figure number, the thousand's place.   Then we'll have 3 choises.   Take "6" and place it on the right of "8", the hundreds place.   We'll have 2 numbers left, 8642 and 8624.

If we take "4" in place of "6", we'll have 2 numbers left, 8462 and 8426.   Or if we take "2" in place of "6", we'll have 2 numbers left, 8264 and 8246.

Thus, we have a set consists of 6 different numbers: {8642,8624,8462,8426,8264,8246}.

In the same manner, we'll have 3 sets consist of 6 4-figure numbers headed by 6,4 and2:

{6842,6824,6482,6428,6284,6248}, {4862,4826,4682,4628,4286,4268},{2864,2846,2684,2648,2486,2468}.

Therefore, we have 6x4=24 combinations in different orders.

CK: On the first choice we'll have 4 possibilities, on the second choise we'll have 3 possibilities, then 2, and finally only one left.   So, we'll have 4x3x2x1=24(=4!) different combinations.   CKD.