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Plz help with this

 

 

Fill in the blanks to make the equation true (Each blank should contain a positive integer.)

 

\binom{n}{k} = \binom{n - 2}{k} + \binom{n - 2}{k - 1} + \binom{n  - 1}{k} + \binom{n - 1}{k - 1} + \binom{n}{k - 1} + \binom{n}{k + 1}

 Jan 28, 2023
 #1
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\(\binom{n}{k} = \binom{n - 2}{k} + \binom{n - 2}{k - 1} + \binom{n - 1}{k} + \binom{n - 1}{k - 1} + \binom{n}{k - 1} + \binom{n}{k + 1}\)

Try using pascal's Identity which states that \(\binom{n}{k} = \binom{n - 1}{k} + \binom{n - 1}{k - 1}\)

https://artofproblemsolving.com/wiki/index.php/Pascal%27s_Identity

hopefully this helps :)

 Jan 28, 2023
edited by YourAverageDummy  Jan 28, 2023

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