Night session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations [video]. Retrieved from https://doi.org/doi:10.7282/T3736QR4
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.
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!].
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)