Answer & Explanation:1. In a race in which seven automobiles are entered and there are no? ties, in how many ways can the first three finishers come? in?2. To win at LOTTO in one? state, one must correctly select 7 numbers from a collection of 50numbers? (1 through 50?). The order in which the selection is made does not matter. How many different selections are? possible?3. The Senate in a certain state is comprised of 53 ?Republicans, 46 Democrats, and 11 Independent.How many committees can be formed if each committee must have 3 Republicans and 2?Democrats?4. You are dealt one card from a standard? 52-card deck. Find the probability of being dealt a diamond.5. A single die is rolled twice. The 36? equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 20.6. In one? lottery, a player wins the jackpot by matching all five numbers drawn from white balls? (1 through 43?) and matching the number on the gold ball? (1 through 34?). What is the probability of winning the? jackpot?7. If you are dealt 5 cards from a shuffled deck of 52? cards, find the probability of getting two queensand three kings.8. A single die is rolled. Find the probability of rolling an odd number or a number less than 3.9. The mathematics faculty at a college consists of 5 professors,12 associate? professors, 11assistant? professors, and 8
instructors. If one faculty member is randomly? selected, find the probability of choosing a professor or an instructor.10. You draw one card from a? 52-card deck. Then the card is replaced in the deck and the deck is? shuffled, and you draw again. Find the probability of drawing an eight the first time and a spadethe second time.11. Consider a political discussion group consisting of 5 ?Democrats, 4 Republicans, and 5Independents. Suppose that two group members are randomly? selected, in? succession, to attend a political convention. Find the probability of selecting no Independents.12. A construction company is planning to bid on a building contract. The bid costs the company 1400. The probability that the bid is accepted is one fourth If the bid is? accepted, the company will make 35,600 minus the cost of the bid.What is the expected value in this? situation?13. You are taking a? multiple-choice test that has 5 questions. Each of the questions has 4answer? choices, with one correct answer per question. If you select one of these choices for each question and leave nothing? blank, in how many ways can you answer the ?questions?14. A club with fifteen members is to choose three? officers: ? president, vice-president, and? secretary-treasurer. If each office is to be held by one person and no person can hold more than one? office, in how many ways can those offices be? filled?