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| Math Central | Quandaries & Queries |
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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
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