Permutation and Combination
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6 papers are set in an examination out of which two are of maths. In how many ways can the paper be arranged so that 2 maths paper are not consecutive?
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Report CancelHi Meena
6 papers can be arranged together by 6! without any restriction. So there are 6*5*4*3*2*1 or 6! ways to arrange them regardless of whether M1 and M2 come together or not.
Now, When M1 and M2 come together, we can think of using a paper clip to clip the two mathematics papers together. Then we have only 5 things, A,B,C,D, and (M1M2) if we clip them together with M1 on top of M2,
or else we have A,B,C,D and (M2M1) if we clip them together with M2 on top of M1. Each of those gives 5! ways each. So that’s 2*5! ways the papers can be arranged with M1 and M2 paper-clipped together.
So the answer is 6! – 2*5! = 720 – 2*120 = 720 – 240 = 480
Let me ask if you need further explaination.
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