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There is a question that goes like this :
The supreme court has given a 6 to 3 decisions upholding a lower court; the number of ways it can give a majority decision reversing the lower court is :

Actually in this question, I can't get the statement what does the statement "6 to 3 decisions upholding a lower court" mean and then what we have to find ?

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There are 9 justices on the U.S Supreme Court. 6 voted in favor of the decision and 3 voted against. –  Grumpy Parsnip Jun 8 '11 at 6:42
    
I say the "6 to 3" clause is irrelevant; all you're being asked for is how many ways the court can give a majority vote in favor of a particular option. –  Gerry Myerson Jun 8 '11 at 6:51
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1 Answer

up vote 2 down vote accepted

The supreme court has 9 members. A "6 to 3" decision means that 6 judges voted with the lower court, and 3 voted against.

To reverse the order, a majority of judges must vote to reverse it. So either 5, 6, 7, 8, or 9 judges must vote to reverse the decision. The question is, how many ways can this happen?

Does that make sense?

HINT: The answer is a 2 power (but that's deceptively non-obvious from the sum).

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on the other hand, it's blindingly obvious that it's a power of $2$ when you consider the total number of ways to vote and the one-one correspondence between votes that uphold and votes that reverse. –  Gerry Myerson Jun 8 '11 at 6:50
    
@Gerry - oh, that's true. ;p –  mixedmath Jun 8 '11 at 6:51
    
ok..I got it. So it must be 9C5 + 9C6 + 9C7 + 9C8 + 9C9. So is the statement "The supreme court has given a 6 to 3 decisions upholding a lower court" is used only to determine total number of judges ? It has nothing to do with rest of the question...right ? –  Happy Mittal Jun 8 '11 at 6:52
    
@Happy: yeah... not every question is a good one... –  mixedmath Jun 8 '11 at 6:56
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