1 Lab a) A standard card deck consists of 52 cards, made up of 13 cards of each of 4 different suits. How many unique 5 card hands exist that are all the same suit? Hint: Does order matter?b) Suppose you are taking a picture of 10 people, 3 of whom are siblings. How many ways can you form the family into a line such that all three siblings are not next to each other.c) How many ways can you order 6 donuts from a doughnut shop with apple, banana and cherry donuts (A,B,C) with at most two apple? Try counting by complement(1) Two fair six-sided dice are thrown. What. is the probability that. the sum of both dice is at least 8'? e) There are 10 socks in a drawer, 5 white and 5 black. Two socks are selected uniformly and at random. What is the probability both drawn socks are the same color?f) Consider an experiment of rolling three fair: sixsided dice. Prove or disprove that the following two events are independent. 0 Probability that the sum is at least 10 0 Probability that the rst dice roll is even