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  1. #1
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    Evaluation

    What formula is used for this problem?

    Evaluate
    20!
    18!
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  2. #2
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    Quote Originally Posted by mike1 View Post
    What formula is used for this problem?

    Evaluate
    20!
    18!
    The "!" denotes the factorial of the number preceeding it. It is the product of
    all the integers less than the number and greater than 1. By convention we take 0!=1.

    So:

    20!= 1x2x3x4x5...x18x19x20

    18!= 1x2x3x4x5...x18.

    So:

    20!/18!=(1x2x3x4x5...x18x19x20)/(1x2x3x4x5...x18)=19x20=380

    RonL
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  3. #3
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    Quote Originally Posted by mike1 View Post
    What formula is used for this problem?

    Evaluate
    20!
    18!
    Hello, Mike,

    use the definition:

    \frac{20!}{18!}=\frac{1 \cdot 2 \cdot 3 \cdot ... \cdot 18 \cdot 19 \cdot 20}{1 \cdot 2 \cdot 3 \cdot ... \cdot 18}

    Cancel equal factors and you'll get: 19 * 20 = 380

    EB
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  4. #4
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    So, what is the difference then if there isn't an ! and it is just to evalute:

    Evaluate
    {11}
    { 3}
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  5. #5
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    Quote Originally Posted by mike1 View Post
    So, what is the difference then if there isn't an ! and it is just to evalute:

    Evaluate
    {11}
    { 3}
    Well this is ambiguous there are plenty of possible meanings for this, but
    I will assume you mean the binomial coefficient or combinations symbol:

    {11 \choose 3}

    also written:

    C^n_k

    This is defined to be:

    {n \choose k}=\frac{n!}{k!\,(n-k)!},

    so in this case we have:

    {11 \choose 3}=\frac{11!}{3!\,8!}=\frac{11 \times 10\times 9}{3 \times 2 \times 1}=165,

    RonL
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