Determine Probability of Video Selection and Impact Evaluation

##### Scenario Designing a video-recommendation push system: selecting k videos from a large inventory and evaluating product impact between friends. ##### Question a) From an inventory of N videos, what is the probability a specific ordered set of k videos is pushed to a user? What about any unordered subset of size k? b) Given an event’s probability, compute its complementary probability and apply it to the video-selection context. c) Should we push the same video to two friends or different videos? Discuss pros, cons, and expected metrics impact. d) Which statistical or machine-learning model would you use for this recommendation problem and why? ##### Hints Use permutation/combination formulas, complementary events, discuss CTR vs. content diversity, and mention models like collaborative filtering or sequence models.