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Two squares of `1xx1` are chosen at random on a chestboard. What is the probability that they have a side in common ?A. `1//18`B. `64//4032`C. `63//64`D. `1//9` |
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Answer» Correct Answer - A `(a)` Total number of ways of selecting two squares `"^(64)C_(2)=(1)/(2)(64xx63)=2016` If the first square happens to be any of the four corner ones, the second square can be chosen in `2` ways. If the first square happens to be any of the 24` squares on the side of the chess board, the second square can be chosen in `3` ways. If the first square happens to be any of the `36` remaining squares, the second square can be chosen in `4` ways. Hence the required number of combinations `=(1)/(2)((4xx2)+(24xx3)+(36xx4))=112` Therefore, the required proability `=1//18`. |
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