# Math Help - Help with Combinations

1. ## Help with Combinations

Hi, I was told once that there is a formula for figuring out different kinda of combinations... I need to know the formula that will figure out the combination that fits into these rules...

I have a keypad, it has numbers from 1 - 9... I have to enter combinations of 4 numbers. The numbers in the combination always have to go from smallest to largest... So I could have 1579, but not 1845... The numbers can't repeat, so I can't have 1157...

What is the formula I would use to figure out how many combinations I could made?

Thank you in advance for any help.

2. Theses are called sorted integers.
${9 \choose 4} = \frac{9!}{4! 5!} = 126 .$

Any set of four digits fits the description.

3. Hi and thank you.
A question, what is the 5! for?
I'm guessing the 9! is for the numbers on the keypad, and the 4! is the number of numbers in a combination...

4. It is a very basic counting rule.
Think about the string 001001011 representing {3,6,8,9}
The string 110010100 represents {1,2,5,7}.
So each such string represents a four-element subset of {1,2,3,4,5,6,7,8,9}.
There are $\frac{{9!}}{{\left( {4!} \right)\left( {5!} \right)}}$ ways to rearrange that string.

5. I'm... more confused now? (sorry) What is a string? I don't understand why one thing leads to another...

6. Originally Posted by AbigailFJ
I'm... more confused now? (sorry) What is a string? I don't understand why one thing leads to another...
All you have to know is that any set of four positive digits gives a number that you want. There are 126 such sets.

Combin(m,k)= $\frac {m!} {(k!)(m-k)!}$