a) A fair dice is rolled 3 times. Calculate the probability that the results are in STRICTLY increasing order. b) A dice is rolled 330 times and their results are written sequentially separated by a comma. Denote by X the expected number of sequences of 3 numbers in increasing order in between commas in this list. Calculate E(X) c) An experiment consists on rolling a dice 3 times, and repeat this until 3 results in increasing order have been obtained. If Y is the total number of rolls, calculate E(Y) Hint: What is the distribution of Y/39