There are p points in a plane, no three of which are in the same straight line with the…

Mathematics · JEE Main · NTA ExamsPermutations and Combinations

There are p points in a plane, no three of which are in the same straight line with the exception of q points which are all in the same straight line. Find the number of straight lines.
  1. \({ }^{\mathrm{a}} \mathrm{C}_{2}\)
  2. \({ }^{\mathrm{a}} C_{2}-{ }^{\mathrm{a}} C_{2}\)
  3. \({ }^{\mathrm{a}} C_{2}-{ }^{\mathrm{a}} C_{2}+1\)
  4. None of these

Answer

(C) ^ a C_ 2 - ^ a C_ 2 +1

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