Exercise 1: Combinatorics (a) We have an album of photos, where 1/3 are Photos of x, 1/2 are photos of y and 1/6 are Christmas photos. Your phone background is being chosen randomly from these photos 3 times per day. 0 1What is the probability, that all 3 photos are Christmas photos? 0 What is the probability, that one from each appears? (b) You are going camping with 3 friends in a tent with 5 possible sleeping positions. How many orders exist, if one of your friends only sleeps in the on either side of the tent. (The one friend doesn't want to lie in the middle). (c) You are running a testing centre, where every 10th test is positive. You are taking 10 samples. How big has the sample size to be, such that the probability that there is at least one positive test is at least 99%