# How many combinations can you make with the numbers 1,2,3?

##### 2 Answers

See a solution process below:

#### Explanation:

The first number in the combination can be any 1 of the 3 number.

The second number can be either of the 2 remaining numbers.

For the final number you would have only 1 choice.

Therefore, the number of combination is:

#1, 2, 3# #1, 3, 2# #2, 1, 3# #2, 3 , 1# #3, 1, 2# #3, 2, 1#

Please see below.

#### Explanation:

We are not told the size of the combinations to be formed. I'll return to this point later.

**Permutations and Combinations**

In a permutation order matters, so the permutation (1 2 3) is not the same as (2 1 3).

In a combination order does not matter so the combination (2 3) is the same as (3 2).

**Combinations with or without repetition**

The question does not say whether we are allowed repetition or not.

So we do not know whether we are to count (1 1 3) as a combination of 3.

We are also not told the size of the combination. But if repetition is allowed then there are infinitely many combinations of all sizes that can be formed.

Therefore, I shall assume that repetition is **not** allowed.

**Without repetition**

Starting with 1 2 3 we can form combinations of size 1 2 or 3.

For

#(n!)/(r!(n-r)!)#

So we have:

That is a total of