How many different four-digit numbers can you make from the digits 1,2,3, and 4 if each digit is used only once?

1234

1324
1432
1243
1423
1342
2134
2143
2341
2314
2431
2413
3124
3142
3241
3214
3412
3421
4321
4312
4123
4132
4231
4213

24
there are 4 numbers...each can be used only once but 6 different ways
6x4=24

This is a problem class known as permutations. There are 4 choices for your first number (i.e, 1,2,3,4)followed by 3 ways to pick the next number since there are only 3 numbers left. This leaves 2 ways to pick the next number and 1 way to pick the remaining number.

4*3*2*1 = 24

I am a 3-digit number.My first digit is a square number.My last digit is 3* my second digit,which is my half my first digit.What am I.

To find out the number of different four-digit numbers that can be made using the digits 1, 2, 3, and 4, where each digit is used only once, we can use the concept of permutations.

A permutation is an arrangement of objects where the order matters. In this case, we are arranging the digits 1, 2, 3, and 4 to form four-digit numbers.

The first digit can be chosen from any of the four available digits (1, 2, 3, or 4). Once the first digit is chosen, there are three remaining digits to choose from for the second digit. Similarly, there are two remaining digits for the third digit and only one digit left for the fourth digit.

So, the number of different four-digit numbers can be calculated as follows:

Number of choices for the first digit = 4
Number of choices for the second digit = 3
Number of choices for the third digit = 2
Number of choices for the fourth digit = 1

To find the total number of arrangements, we multiply the number of choices for each digit:

Total number of arrangements = 4 * 3 * 2 * 1 = 24

Therefore, you can make a total of 24 different four-digit numbers using the digits 1, 2, 3, and 4, where each digit is used only once.