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Math Help - combo's

  1. #1
    brian
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    combo's

    how many diffrent combonations of 4 can I make with 20 numbers
    EX:1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18-19-20

    1-2-3-4 AND HOW WOULD I put them into combos
    1-2-3-6
    ETC....
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  2. #2
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    Quote Originally Posted by brian View Post
    how many diffrent combonations of 4 can I make with 20 numbers
    EX:1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18-19-20

    1-2-3-4 AND HOW WOULD I put them into combos
    1-2-3-6
    ETC....
    It depends whether,

    1,2,3,4 is same as 1,2,4,3 or different.


    If different then the answer is N=20\cdot 19\cdot 18\cdot 17. Otherwise,
    N/24
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  3. #3
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    Hello, brian!

    Have you had no instruction on Permutations and Combinations?


    How many different 4-number combinations can be made from a set of 20 numbers?

    Ex: 1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18-19-20

    1-2-3-4, 1-2-3-6, etc.

    Identical problem: There are 20 different CDs on sale.
    . . . . . . . . . . . . . You have enough money to buy four of them.
    . . . . . . . . . . . . . In how many ways can you select four CDs?

    Since you are choosing the CDs and tossing them in a shopping bag,
    . . the order of the CDs is not important.
    Hence, this is a "combinations" problem.

    The Combination Formula says: . _{20}C_4 \:=\:\binom{20}{4} \:=\:\frac{20!}{4!16!} \:=\:4,845 ways.


    The derivation goes like this:

    You have 20 options for your first choice,
    . . . .and 19 options for your second choice,
    . . . .and 18 options for your third choice,
    . . . .and 17 options for your fourth choice.

    It seems that you have: . 20 \times 19 \times 18 \times 18 \:=\:116,280 possible choices.

    But this long list includes choices like: \{A,B,C,D\} and \{B,D,C,A\}
    . . Since the order is not important, these two selections are identical.

    Since 4 objects can be arranged in 4! = 24 different orders,
    . . our number is too large by a factor of 24.
    . . Our list has 24 times as many choices as it should have.

    Hence, the corrected answer is: . \frac{116,280}{24} \,=\,4,845

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