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

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 â€‹women?
5. The Senate in a certain state is comprised of 58 â€‹Republicans,38 â€‹Democrats, and 44
Independents. How many committees can be formed if each committee must have 33 Republicans and 22 â€‹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 â€‹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 â€‹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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