Binomial coefficients are a powerful counting tool with which many undergraduate mathematics students are unaware. This talk will illustrate how binomial coefficients can be used to enumerate decreasing numbers and peak numbers. A surprising connection between the number of peak numbers and the often forgotten identity 1^2 + 2^2 . . . + n^2 = [n(n+1)(2n+1)]/6 will be revealed. Has this piqued your interest?
