Binomial Coefficients Problem I have to evaluate the following but I am not sure how to do it. My professor went over it briefly trying to get it in before the end of the semester but did not explain it very well. I'm not even sure of where to begin.
$$ \sum\limits_{k=7}^{60}\binom{k-2}{20}. $$

The binomial identity
$$
\sum_{k=i}^{n-j}\binom{k}{i}\binom{n-k}{j}=\binom{n+1}{j+1}
$$
setting $j=0$, says that
$$
\sum_{k=20}^{58}\binom{k}{20}=\binom{59}{21}
$$
which is your sum after ignoring terms that are $0$.
