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 be​done?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.

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