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12 chocolates are placed in straight line. How many ways we can choose four so that no 2 of them are next to eachother?

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There are 12 different chocolates placed on a table along a straight line. In how many ways can a person choose 4 of them such that no 2 of the chosen chocolates lie next to each other?

posted Feb 13, 2017 by anonymous

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1 Answer

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Out of 12 chocolate bars only 4 of them are chosen, which means 8 of them are not selected at a time.
So to find the required answer we have to evaluate how many ways we can fill the 4 bars of chocolate around the spaces of the un selected chocolate bars. There are 9 such spaces so the required answer is
9C4 = 126. ie., there are 126 ways that the chocolate bars can be selected such that no 2 bars are next to each other

answer Feb 22, 2017 by Tejas Naik
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