Meaning of the question 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 ?
 A: 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).
A: Got it . So There are 9 judges in total and 6 are voting for the decision of lower court and 3 are voting against . So in how many ways the decision can be reversed . 
It can by 5 votes for or 6,7,8 and the whole 9 to get majority so , 
9C9+9C8+9C7+9C6+9C5 
=1+9+36+84+126 =256 is the  answer
A: Since there are $9$ judges, there is no case of a tie (equal number of votes for and against). Thus, the number of ways that "for" gets a majority is equal to the number of ways that "against" gets a majority, and therefore, each must be half of the total number of ways to vote.
The total number of ways to vote is, of course, $2^9 = 512$ (as there are nine judges and each independently votes for or against).
So, the answer is ${256}$.
