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Math Help - How to rewrite as a single combination

  1. #1
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    How to rewrite as a single combination

    How do you rewrite 10C7 + 10C8
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  2. #2
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    Hello, nafiro!

    \text{How do you write: }\:_{10}C_7 + _{10}\!C_8\:\text{ as a single combination?}

    We have: . \frac{10!}{7!\,3!} + \frac{10!}{8!\,2!}

    Get a common denominator: . {\color{red}\frac{8}{8}}\cdot\frac{10!}{7!\,3!} + \frac{10!}{8!\,2!}\cdot{\color{red}\frac{3}{3}} \;\;=\;\; \frac{8\cdot10!}{8!\,3!} + \frac{3\cdot10!}{8!\,3!}<br />


    And we have: . \frac{8\cdot10! + 3\cdot10!}{8!\,3!} \;\;=\;\;\frac{11\cdot10!}{8!\,3!} \;\;=\;\;\frac{11!}{8!\,3!} \;\;=\;\; _{11}C_8


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