1) How many 5 digit numbers exist, whose first, and last digits are prime numbers and the middle is an odd digit? Eg. 54365, 27913, 74342 [2 marks] 2) Five basketball players randomly line up for a photo. What is the probability that the shortest and tallest players are not side by side? [2 marks] 3) A committee of 5 is to be selected from 4 Biologists, 5 Chemists and 12 Physicists. How many ways can this be done if they have at least 3 Biologists on the committee? [2 marks] 4) How many ways can you spell LEBRON starting from the top and reaching the bottom? [2 marks] E 5) The odds in favor of Dan going to the party tomorrow is 11:3. The odds against Jill going to the party tomorrow is 15:2. Assume these are independent events. What is the probability either Dan or Jill will go to the party? [2 marks]