Question 961540: A committee of four is to be selected from a group of sixteen people. How many different committees are possible, given the following conditions?
a) One person is the chair, and the rest are general members?
b) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.
How many five card poker hands consisting of all hearts are possible?
How many five card poker hands consisting of all cards of the same suit are possible?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A committee of four is to be selected from a group of sixteen people. How many different committees are possible, given the following conditions?
a) One person is the chair, and the rest are general members?
Pick a chairman:: 16 ways
Pick 3 others:: 15C3 = 455 ways
Ans: 16*455 = 7200
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b) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.
Ans: 16*15*14*13 = 43600
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How many five card poker hands consisting of all hearts are possible?
Ans:: 13C5 = 1287
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How many five card poker hands consisting of all cards of the same suit are possible?
Ans: 4*13C5 = 5148
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Cheers,
Stan H.
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