Hi, I am in difficulty when I kept trying to do this question.

Could you give me a help to solve this question?

Thank you so much.

1. Suppose we have 10 identical candies and we distribute it randomly among Alice and Bob (it is possible to get no candy). Represent carefully the sample space of this experiment. 2. Let M be the set of all 2 x 3 matrices where each entry is either 0 or 1. Pick one such matrix uniformly at random. What is the chance that no two columns are equal? 3. Suppose a deck of 52 cards is shuffled uniformly at random and put on a table. What is the probability that each king is directly on top of an ace (i.e. king and ace are adjacent and the king is on top of the ace)!? 4. Suppose we color 9 balls, all of different sizes with 4 colors. Choose one such coloring uniformly at random. What is the probability that at least two balls will have different colors? Answer the same question if the balls are all of the same size and are in a bag (ordering of the balls is unimportant). 5. Suppose the letters of the word UNCOPYRIGHTABLE is arranged uniformly at ran- dom. What is the chance that B comes before C in the arrangement? (Hint: Maybe counting the total number of such possibilities is not the optimal method.) 6. In a shop there are 3 different types of candies. How many ways are there to buy 6 candies? What is the probability that all those candies are of the same type if a choice among the above is made uniformly at random? There are 4 different kings and 4 different aces in a deck of 52 cards