How many numbers can be formed using the digit 1 2 3 4?

Answer 1

If each digit can be used only once, you can form 24 four digit numbers:

1234 1243 1324 1342 1423 1432 2134 2143 2314 2341 2413 2431 3124 3142 3214 3241 3412 3421 4123 4132 4213 4231 4312 4321

If you are not required to use all 4 digits you can form an additional 24 three digit numbers, 12 two digit numbers, and 4 one digit numbers:

123 124 132 134 142 143 213 214 231 234 241 243 312 314 321 324 341 342 412 413 421 423 431 432

12 13 14 21 23 24 31 32 34 41 42 43

1 2 3 4

You can calculate the expected numbers by using the number of permutations. For four digits, you can select any one of 4 digits for the first digit, leaving 3 possibilities for the next digit, 2 remaining to choose for the third digit, and just one possibility for the last digit: 4x3x2x1 = 24

Likewise choosing 3 digits from 4 gives 4x3x2 = 24 and choosing 2 from 4 digits gives 4x3 = 12. Obviously if you are choosing just one digit, you only have 4 choices.

Answer 2

If you are only allowed to use each digit once, you can form 24 three digit numbers from the digits 1, 2, 3, and 4.

123 124 132 134 142 143 213 214 231 234 241 243 312 314 321 324 341 342 412 413 421 423 431 432

You can calculate the expected numbers by using the number of permutations. For a 3 digit number you can select any one of 4 digits for the first digit, leaving 3 possibilities for the next digit, and 2 remaining to choose for the third digit:

4x3x2 = 24

Answer 3

6. 123, 132, 213, 231, 312, 321.

Answer 4

4 x 3 x 2 = 24 of them