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 Question from shipra, a student: In an Exam having 9 papers, a candidate is unsuccessful if he fails in more number of papers than the number of papers he passes.So in how many ways can he be unsuccessful?

Hi Shipra,

If the candidate fails more papers than he passes and there are 9 papers, this mean he would be unsuccessful if he fails 5 or more papers. So in other words he could fail 5 out of 9 papers, 6 out of 9 papers, 7 out of 9 papers, 8 out of 9 papers or all 9 papers to be unsuccessful. For each scenario, there are many different combinations of papers to pass or fail. To put it into mathematical terms if he failed 5 papers out of 9

9C5 = 126

There are 126 different ways to fail 5 papers out of a group of 9.

Once you figure out how many combinations are for each unsuccessful scenario, add all of the scenarios together to find the total.

Hope this helps,

Janice

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.