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Math Help - Help with Combinations

  1. #1
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    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.
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  2. #2
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    Theses are called sorted integers.
    {9 \choose 4} = \frac{9!}{4! 5!} = 126 .

    Any set of four digits fits the description.
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  3. #3
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    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...
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  4. #4
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    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.
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  5. #5
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    I'm... more confused now? (sorry) What is a string? I don't understand why one thing leads to another...
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  6. #6
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    Quote Originally Posted by AbigailFJ View Post
    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)!}
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