how many combernations are there between numbers 1 to 10

If you mean all combinations taken 1 at a time plus those taken 2 at a time plus ... plus those taken 10 at a time, then:

$$\sum_{k=1}^{10}nCr(10,k)=1023$$

(I've assumed "between" is inclusive of 1 and 10).

.

Ha, i thought it'll be like.

 2, 3, 4, 5, 6, 7, 8 ,9

Are all the numbers between 1-10.

8 is the amount.

$${\mathtt{8}}{!} = {\mathtt{40\,320}}$$

40320 combinations.

Hi MathGod,

You and Alan have answered very different questions.

Alan has answered a combination question and you have answered a permutation question.

 I will give you a much more simple question to try and show you the difference

1a) How many Combinations are there of 2,3,4,5,6,7,8,9  All numbers must be used just once.

The answer to this is 1  

This is because order does not matter so there is only one way to choose 8 numbers from 8 numbers!

1b) How many Permutations are there of 2,3,4,5,6,7,8,9  All numbers must be used just once.

This is the question you answered and your answer of 8! was correct for this question.

With permutations the order matters that is why there are so many answers.

2A    How many combinations of 2 digits can you get from  4,5,6

Well lets see, there is   4,5   and   4,6   and  5,6   That is it!  The answer is 3 combination

2B   How many permutations of 2 digits can you get from  4,5,6

Mmm,      4,5    and   5,4     they are different for permutations because order counts!

there is also     4,6   and   6,4    and   5,6  and     6,5      and that is it.  SO there are   6 permuations 

Hi Melody,

I'm glad you posted on here.

Literally 2 minutes ago (when I came online) I searched this post to see if anyone can answer my question (in particular you!)

I was wondering this and i doubt that anyone would respond as it's a very old post.

Thank you for your explanation 

Now I can see the difference between combinations and permutations easily.

I have two questions. 

1). The word permutation, can it be used in a sentence the way combination is used? (I find it hard using the right words)

2). You said the answer is 1 (for example 1), however Alan got 1023 ?

Alan answered a much more complicated question.

He was using the numbers 1,2,3,4,5,6,7,8, 9, and 10

There are 10 ways to chose just one number  

That is 10C1 and you would put it into the web2 calc as  nCr(10,1)

There are 10C2 ways to choose 2 numbers  that is nCr(10,2)

...

there are 10C10 ways to chose 10 numbers (this will be = 1)  but it can go into the calc as  nCr(10,10)

Alan used this symbol      $$\sum$$      it means "sum of"

so his answer

$$\sum_{k=1}^{10}nCr(10,k)=1023$$

is the same as     10C1+10C2+10C3+10C4+10C5+10C6+10C7+10C8+10C9+10C10

I'm not familiar with nCr and C1, C2 etc. 

nCr 

$$^5C_2$$    would be entered into the web2 calc like this    nCr(5,2) 

It means, how many ways can 2 things be chosen from 5 if order does not count

(the C stands for Combinations).  

I'll enter it now,  it adds the maths but you don't need to worry about that.

$${\left({\frac{{\mathtt{5}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{10}}$$           See, there are 10 ways

Oh, cool!