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Compute
binom{5}{3} + binom{6}{3} + binom{7}{3}

 Dec 17, 2022
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Compute \(\dbinom53+\dbinom63+\dbinom73\).

USE THE HOCKEY STICK THEOREM (See this).

 

 

See that \(\dbinom53+\dbinom63+\dbinom73=\dbinom84-\Bigg[\dbinom43+\dbinom33\Bigg]=\dbinom84-\Bigg[\dbinom41+\dbinom30\Bigg]=70-(4+1)=\boxed{65}\)

 Dec 18, 2022

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