PreCalculus Short Task Exercise Mathes Questions

Answer the following questions in a Word document and upload the document to the appropriate drop box.1) A combination lock will open when you select the right choice of three numbers. How many possible lock combinations are there, assuming you can choose any number from 0 and 35?a) Assume the numbers must be distinct.b) Assume they may be the same.2) Eleven sprinters qualify for the finals in the 150-meter dash at a national track meet. In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.3) The employees of a company work in six departments: 15 are in sales, 50 are in research, 12 are in marketing, 20 are in finance, and 100 are in production. The payroll clerk loses one employee’s paycheck. What is the probability that the employee works in the research department? 4) The deck for a card game contains 30 cards. 10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards. Each player is randomly dealt a five-card hand. a) What is the probability that a hand will contain exactly two wild cards? b) What is the probability that a hand will contain two wild cards, two red cards, and one blue cards? (9.7-44)5) A fire department keeps two rescue vehicles. The probability that a specific vehicle is available at any given time when needed is 90%. Also, the availability of one vehicle is independent of the availability of the other. Find: a) The probability that neither vehicle is available at a given time b) The probability that at least one vehicle is available at a given time. c) The probability that both vehicles are available at a given time.