# Using all four digits 1,2,3,4 how many four-digit telephone extension numbers can write?

**Vibran51**- 6 Answers

Although the answer is permutation, the answer is not 24. This is because the numbers don't need to be unique and non-repetitive, or do they? For example, 3333 is still an extension number although 3 is repeated four times. Let me explain with the help of a picture.

You have 4 choices - 1, 2, 3 and 4. You should make numbers which consists of four digits. Let the digits be a,b,c and d. For a, you have 4 options - 1, 2, 3 and 4. For b, you still have four options left because the digits in telephone numbers should not be unique. So, you have four choices left for all these four places - 1, 2, 3, 4.

So the answer would be 4 x 4 x 4 x 4 = 256. The answer would have been 24 if the digits should have not been repeated.

When using al four numbers at once and each only once, the 4-digit combination of numbers one, two, three and four results in a total of 24 number combinations.

You can find them below, listed in order of number combination. Thus, the list begins with number one and finishes with the number four:

1234,

1243,

1324,

1342,

1423,

1432,

2134,

2143,

2314,

2341,

2413,

1431,

3124,

3142,

3214,

3241,

3412,

3421,

4123,

4132,

4213,

4231,

4312,

4321.

You can find the number of extensions by mathematical combination theory. That theory is called factorial. It mean you multiply consecutive numbers of digits and get the number of positions that can be arranged by this number.

If you take factorial of 4 digits number that is 1,2,3,4, then the answer will be 4*3*2*1= 24. It means that you can orange four digit number extension in 24 different ways.

As telephone numbers can contain repeating numbers, you can have four options for four times. So, there is no significance of factorial here.

The answer would be 4 x 4 x 4 x 4 = 256 telephone numbers. As telephone number contain repeating digits, one is used does not mean we cannot use it again. So, the answer is 256 and not 24 as said above.

This is a small example of combination theory in mathematics.

The answer is, 4! = 4 x 3 x 2 x 1 = 24

So, using 1,2,3 and 4, one can write 24 kinds of four-digit telephone extension numbers without any repetition of those numbers.

Thats a very good question.

Its answer is the permutation

of this 4 numbers,1,2,3,4.

And its answer is 4!=24

n!=(n-1)! where n>=1;

1!=1.

4!=4*3*2*1=24