Math Is Fun Forum

Jrzygal

Member

Registered: 2016-03-25

Posts: 4

Help with combinations

I need to figure out how many possible number combinations can be formed using 0,1,2,3,4,5,6,7,8,9 that start with 0 and end with 6 with no repeats.  I'm not a "math person" so need simple explanation.  Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with combinations

Hi;

Start by fixing the two end positions:

0 _ _ _ _ _ _ _ _ 6

You have 8 _'s to fill in with 8 numbers that are left {1,2,3,4,5,7,8,9}. Those eight numbers can be arranged in 8! ways so the answer is 40320.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jrzygal

Member

Registered: 2016-03-25

Posts: 4

Re: Help with combinations

Thanks. So sorry I forgot to mention that I only need 4 digit combinations that start with 0 and end with 6 and no repeats so 0_ _6.  (Using 0 -9). Sorry again

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Help with combinations

Since we already used a

and a

, there are only

numbers we can use. So we have

different combinations.

Jrzygal

Member

Registered: 2016-03-25

Posts: 4

Re: Help with combinations

Thanks for your response. As  I mentioned in my original post I'm not a "math person" so I need further guidance. I need to write these combinations out on paper. What is the easiest way to go about this?  Would I start out with

0 1 2 6
0 1 3 6
0 1 4 6

Could you please start me off?  Thanks in advance

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Help with combinations

Yes, that seems to work out. Just continue going replacing the hundreds place with a number one higher than the original one.

I listed them out, and got

different combinations.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with combinations

Hi;

Here is the entire list

{0,1,2,6}
{0,1,3,6}
{0,1,4,6}
{0,1,5,6}
{0,1,7,6}
{0,1,8,6}
{0,1,9,6}
{0,2,1,6}
{0,2,3,6}
{0,2,4,6}
{0,2,5,6}
{0,2,7,6}
{0,2,8,6}
{0,2,9,6}
{0,3,1,6}
{0,3,2,6}
{0,3,4,6}
{0,3,5,6}
{0,3,7,6}
{0,3,8,6}
{0,3,9,6}
{0,4,1,6}
{0,4,2,6}
{0,4,3,6}
{0,4,5,6}
{0,4,7,6}
{0,4,8,6}
{0,4,9,6}
{0,5,1,6}
{0,5,2,6}
{0,5,3,6}
{0,5,4,6}
{0,5,7,6}
{0,5,8,6}
{0,5,9,6}
{0,7,1,6}
{0,7,2,6}
{0,7,3,6}
{0,7,4,6}
{0,7,5,6}
{0,7,8,6}
{0,7,9,6}
{0,8,1,6}
{0,8,2,6}
{0,8,3,6}
{0,8,4,6}
{0,8,5,6}
{0,8,7,6}
{0,8,9,6}
{0,9,1,6}
{0,9,2,6}
{0,9,3,6}
{0,9,4,6}
{0,9,5,6}
{0,9,7,6}
{0,9,8,6}

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jrzygal

Member

Registered: 2016-03-25

Posts: 4

Re: Help with combinations

Thanks so much for the list bobbym!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with combinations

Hi;

You are welcome.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.