Night session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations

This is the third of seven clips from the night session. The four students (Ankur, Jeff, Michael, and Romina) investigate the reason for dividing n! by (n-x)! and x! when calculating “n choose x.” In explaining the specific example of “5 choose 2,” they use two analogies: 1) arranging five people on a line when you are concerned about the positions of only two of the people and 2) counting the number of 5-tall towers having exactly two cubes of one color. Notes: “Choose” notation is the notation for counting the number of combinations; “n choose r” gives the number of ways of selecting subsets containing r objects from a set containing n objects. When counting combinations, the order of selection is irrelevant. “n choose r” is equal to n!/[(n – r)!r!].Transcript is also available.Robert B. Davis Institute for Learning. (1999). Night session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations. [video]. Retrieved from http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000055282Available in QuickTime streaming and downloadable Flash digital video files