Answer & Explanation:1. In a race in which five automobiles are entered and there are no ties, in how many ways can the first three finishers come in?2.An election ballot asks voters to select two city commissioners from a group of fourcandidates. In how many ways can this bedone?3. To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 48numbers (1 through 48).The order in which the selection is made does not matter. How many different selections are possible?4. In how many ways can a committee of five men and five women be formed from a group of ten men and twelve women?5. The Senate in a certain state is comprised of 58 Republicans,38 Democrats, and 44Independents. How many committees can be formed if each committee must have 33 Republicans and 22 Democrats?6.A city council consists of eight Democrats and seven Republicans. If a committee of fourpeople is selected, find the probability of selecting two Democrats and two Republicans.7. If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability of getting two queens and three kings.8. License plates in a particular state display 2 letters followed by 2 numbers. How many different license plates can be manufactured for this state?9. A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 11 stocks?10. A club with eighteen 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?11. At a benefit concert, ten bands have volunteered to perform but there is only enough time for six of the bands to play. How many lineups are possible?12. In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 41) and matching the number on the gold ball (1 through 32). What is the probability of winning the jackpot?13. A box contains 17 transistors, 3 of which are defective. If 3 are selected at random, find the probability that: a. All are defective.b. None are defective.
