Hi, I got stuck in this questions. Can you help me answer this. Prove and show your solutions please. Thank you.

1.

How many different letter arrangements can be obtained from the letters of the word statistically, using all the letters?A lot of n items contains k defectives, and m are selected randomly and inspected. How should the value of m be chosen so that the probability that at least one defective item turns up is .90? Apply your answer to (a) n = 1000, k = 10, and (b) n = 10,000, k = 100.A deck of 52 cards is shuffled thoroughly. What is the probability that the four aces are all next to each other?A standard deck of 52 cards is shuffled thoroughly, and n cards are turned up. What is the probability that a face card turns up? For what value of n is this probability about .5