Dennis J Fox, Math/Science, McLeod School and Turning Point Academy
Hand shake problems or the combination of things taken 2 at a time are found in many areas of mathematics science and life. This would include setting up tournaments, where everyone plays each other once, and pairings. The numbers are part of a binomial expansion Co it represent 2 of terms when n>2 and a diagonal for Pascal Triangle…
These lessons start with the idea of nine Supreme Court Justices, who shake hands at the beginning of each session, which is a custom almost 100 years old; and the question how many handshakes does it take? This eventually leads in the lesson to ‘How many combinations of ‘n’ things taken 2 at a time, The students discover the answers to several questions involving this, different methods of finding an answer and eventually that nCr is equal to (n(n-1))/2. The nine justices do a total of 36 handshakes.