Permutation 1
In maths paper there is a question on "Match the column" in which column A contains 6 entries & each entry of column A corresponds to exactly one of the 6 entries given in column B written randomly. 2 marks are awarded for each correct matching & 1 mark is deducted from each incorrect matching. A student having no subjective knowledge decides to match all the 6 entries randomly. Find the number of ways in which he can answer, to get atleast 25 % marks in this question.
The answer is 56.
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1 solution
This is a derangement question. We can get 0,1,2,or 3 wrong only otherwise marks will be less than 25%. For 1 wrong , there is no way.For 2 wrong, choose any 2 i.e ( 2 6 ) = 1 5 and then multiply by 1(as there is only 1 way to get these 2 wrong). Total cases till now: 15... For 3 wrong, choose 3 i.e. ( 3 6 ) = 2 0 and then multiply by 2(there are 2 ways to get "all" 3 wrong) ,Total cases till now: 55... and the last case is that he marks all correct. Thus the answer is 56.