A TV show has 26 episodes. Due to the lack of time, you can onlywatch 5 of them. However, in order to get a gist of what the showis about, you do not want to watch any two consecutive episodes. How many selections of 5 episodes are there with no two consecutiveepisodes chosen? Assuming that the order of selection is irrelevant.(Hint:this is a Stars and Bars problem)

Step-by-step explanation:

Recall that: The number of combination to select any k consecutive element from n consecutive term is given by the equation

where:

n = 26

k = 5

Therefore, there are 26334 selection of 5 episodes with no two consecutive episodes chosen

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.