1. In a race in which five automobiles are entered and there are noâ€‹ ties, in how many ways can the first three finishers comeâ€‹ in?

2.An election ballot asks voters to select two city commissioners from a group of four

candidates. In how many ways can this beâ€‹done?

3. To win at LOTTO in oneâ€‹ state, one must correctly select 7 numbers from a collection of 48

numbersâ€‹ (1 through 48â€‹).The order in which the selection is made does not matter. How many different selections areâ€‹ 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 four

people isâ€‹ selected, find the probability of selecting two Democrats and two Republicans.

7. If you are dealt 5 cards from a shuffled deck of 52â€‹ 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 thisâ€‹ state?

9. A stock can goâ€‹ up, goâ€‹ down, or stay unchanged. How many possibilities are there if you own

11 â€‹stocks?

10. A club with eighteen members is to choose threeâ€‹ officers: â€‹ president, vice-president, andâ€‹ secretary-treasurer. If each office is to be held by one person and no person can hold more than oneâ€‹ office, in how many ways can those offices beâ€‹ filled?

11. At a benefitâ€‹ concert, ten bands have volunteered to perform but there is only enough time for

six of the bands to play. How many lineups areâ€‹ possible?

12. In oneâ€‹ lottery, a player wins the jackpot by matching all five numbers drawn from white ballsâ€‹ (1 through 41â€‹) and matching the number on the gold ballâ€‹ (1 through 32â€‹). What is the probability of winning theâ€‹ jackpot?

13. A box contains 17 â€‹transistors, 3 of which are defective. If 3 are selected atâ€‹ random, find the probability that:

a. All are defective.

b. None are defective.

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