You have many cans of food to organize on a shelf in your pantry. You have 3 cans of soup, 4 cans of beans ,and 5 cans of tomato sauce. Assume that the cans of each type differ in variety . (for example, the cans of soup are chicken noodle, clam chowder and minestrone)
a) How many distinct ways can you arrange these cans on the shelf?
b) What is the probability that the last can is one of the tomato sauce?
c) What is the probability that none of the cans of soupare next to each other?
d) What is the probability that the first three cans are beans?