1 (a) If 14 women compete in the marathon at the Olympics, inhow many different ways can the gold, silver and bronze medals beawarded?

(b) If a three person committee is chosen at random from a groupof 15 people, how many different committees are possible?

(c) In a new lottery game called "Minibucks", you select fournumbers between 1 and 28. If you match all four numbers with thefour numbers chosen by the lottery that day, you win the jackpot.(It doesn't matter whether the order that the lottery selected thenumbers matches the order that you selected the numbers). What isthe minimum number of different Minibucks tickets you would need tobuy for one drawing in order to be 100% certain to win the jackpotfor that drawing?

(d) In a new lottery game called "Minibucks version 2", youselect four numbers between 1 and 25. If you match exactly three ofyour numbers with the four numbers chosen by the lottery that day,you win $5. What is the probability that you win this prize? Writeyour answer as a decimal accurate to four decimal places.

(e) A drawer contains 16 white socks and 6 black socks. Twodifferent socks are selected from the drawer at random. What is theprobability that both of the selected socks are white? Write youranswer as a decimal accurate to three decimal places.

(f) According tohttps://www.cologuardtest.com/meet-cologuard/how-effective-is-cologuard(Links to an external site.) , if a person with colon cancer isgiven a Cologuard test, the probability that colon cancer isdiagnosed by the test is 92%. If a person without colon cancer isgiven a Cologuard test, the probability that colon cancer isincorrectly diagnosed by the test is 13%. (This means that theprobability of a false positive test result is 13%, and the test issaid to have 87% specificity). Suppose that 2.5 % of the populationactually has colon cancer. If a person is diagnosed as having coloncancer based on a Cologuard test, what is the probability that theperson actually has colon cancer? Write your answer as a decimalaccurate to three decimal places.