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?

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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 four
candidates. In how many ways can this be​done?

3. To win at LOTTO in one​ state, one must correctly select numbers from a collection of 48
numbers​ (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 44

IndependentsHow many committees can be formed if each committee must have 3Republicans and 2​Democrats?

6.A city council consists of eight Democrats and seven Republicans. If a committee of four
people is​ selected, find the probability of selecting 
two Democrats and two Republicans.

7. If you are dealt 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 letters followed by 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, of which are defective. If are selected at​ random, find the probability that: 

a. All are defective.

b. None are defective.

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