C. Solve the following problems. Show all pertinent solutions. 1. In how many ways can a student answer an exam if out of the 6 problems he is required to answer only 5? 2. In a given examination a student is required to answer 5 out of the 7 questions including 3 of the first 4 questions. In how many can he answer the examination? 3. A box contains 3 black and 5 red balls. In how many ways can 2 balls be drawn from the box such that 1 is black and 1 is red? 4. A lot contains 20 electric bulbs 5 of which are defective. In how many ways can 4 bulbs be taken for inspection such that a. no defective electric bulb is included? b. 2 of the defective bulbs are included? c. all of the defective bulbs are included