A test consists of 4 sections. Each section has a maximum of 45 marks. What is the number of ways in which a student can qualify in the test, if the qualifying mark is 90? x1+x2 +x3 +x4 = 90
Like Prof Peterson I am tired of trying to figure out what your questions really should read.
I answered this question exactly as you wrote it. I posted the solution hoping you would see that you would see that method give too large numbers. If your professor gives from one point to 45 points for each of the four sections (that is the way you posted).
You told us nothing about how the points are awarded. Is it that
on each of four sections one can earn from zero to forty-five points.
If so then the generating function is indeed [imath]{\left( {\sum\limits_{k = 0}^{45} {{x^k}} } \right)^4}[/imath]
SEE THE EXPANION which contains [imath]60,906x^{90}[/imath].
So there are [imath]60,906[/imath] ways to earn a ninety. But look at all the very large ways one can earn ninety or above. Add those up and get one huge number! Now because numbers are so large, I really doubt that this interpretation of the structure of the test is correct.
I think that you translate from some language other that English. If that is the case, please get help with the exact wording of this question.
Otherwise, go with the answer provided.
