Powerball is played in forty-three states, the District of Columbia, and the U.S. Virgin Islands. It involves selecting any five of the numbers from 1 to 59, plus a “powerball number,” which is any one of the numbers from 1 to 39. Find the probability of winning the first prize by selecting all numbers correctly.
Assume that you and 15 of your friends have formed a company called Net-Media, and internet music and video provider. A committee consisting of a president, a vice president, and a three-member executive board will govern the company. In how many different ways can this committee be formed.