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Combinations and permutations
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1. A group consists of six men and seven women. Six people are selected to attend a conference.

a.       In how many ways can six people be selected from this group of thirteen​?

b.      In how many ways can six women be selected from the seven ​women?

c.       Find the probability that the selected group will consist of all women.

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



If you are dealt 5 cards from a shuffled deck of 52​ cards, find the probability of getting two queens and three kings.


You are taking a​ multiple-choice test that has 7 questions.  Each of the questions has 5 answer​ choices, with one correct answer per question.  If you select one of these choices for each question and leave nothing​ blank, in how many ways can you answer the​ questions?  




License plates in a particular state display 2 letters followed by 2 numbers.  How many different license plates can be manufactured for this​ state?  




A stock can go​ up, go​ down, or stay unchanged.  How many possibilities are there if you own 6 ​stocks? 


A club with fourteen 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?




At a benefit​ concert, eight bands have volunteered to perform but there is only enough time for five of the bands to play.  How many lineups are​ possible?

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Combinations and permutations
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