a) Find the number of ways of arranging all of the letters of the word TORONTO if:
1. there are no restrictions [3 marks]
2. the R and N cannot be together [3 marks]
b) Suppose that 1 out of 50 cards in a scratch-and-win promotion give a prize.
1. What is the probability that you will win ON your fourth try? [4 marks]
2. What is the probability of winning WITHIN your first four tries? [4 marks]
c) Given a mean of 50 and a standard deviation of 20, What does P(x<55) equal? [4 marks]
d) The letters of TEACH are placed in a bag and picked out one at a time randomly. What is the probability that when placed in a line in the order that they are picked, they will spell CHEAT?
[5 marks]