DescriptionThis 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.
“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!].
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Related Publication Type: Dissertation Label: Ed.D. dissertation references the video footage that includes Night session, Pascal's Identity, clip 3 of 7 Detail: Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection. Author: Uptegrove, Elizabeth B. (Rutgers Graduate School of Education)