Subject: number combination
Who are you: Student
how can I find out all the different combinations for the numbers 8168
example 8168, 8868, 1688,1886,6818 etc.
how many are their.
Suppose first that the digits are 7, 1, 6 and 8, that is all different, and you want to construct a 4 digit number from them, using each digit exactly once. To start you have 4 choices for the first digit. Whatever choice you make you have 3 choices for the second digit so there are 4 3 choices for the first two digits. Again, whatever 2 digits you have chosen you are left with 2 choices for the third digit and then the last digit is whatever is left. Thus in total you have 4 3 1 1 = 24 possible 4 digit numbers from 7, 1, 6 and 8.
Now look at the 24 numbers you have. You can arrange them in pairs where a pair has the 1 and 6 in the same place and the 7 and 8 interchanged. For example 1678 and 1687 are a pair and 7186 and 8176. If you now replace each 7 with an 8 to return to your original problem then each member of these pairs becomes the same number. Thus you have only 24/2 = 12 possible numbers from the digits 8, 1, 6 and 8.