. Suppose you have 5 multiple-choice problems, each one has 4 choices. How many different ways can you answer these problems? . At a company with 35 engineers, the boss will be choosing 5 to go to a conference. How many different groups of 5 members are there to choose from? . From a group of six pro grammable and eight data base designer, five people are chosen at random to make a committee. Find the probability that there are more programmable chosen than designer. . A software package consists of 12 programs, ve of which must be upgraded. If 3 programs are randomly chosen for testing. Find the probability of the following (i) only one program out of the 3 program chosen need to upgrade. (ii) all of them need to upgrade. (iii) at least two programs out of the 3 program chosen need to upgrade