Compute binom{5}{3} + binom{6}{3} + binom{7}{3}
Compute \(\dbinom53+\dbinom63+\dbinom73\).
USE THE HOCKEY STICK THEOREM (See this).
See that \(\dbinom53+\dbinom63+\dbinom73=\dbinom84-\Bigg[\dbinom43+\dbinom33\Bigg]=\dbinom84-\Bigg[\dbinom41+\dbinom30\Bigg]=70-(4+1)=\boxed{65}\)
