gs1easy

In a tournament 14 teams play league matches. If each team plays against every other team once only then how many matches are played ?

  1. A.105
  2. B.91
  3. C.85
  4. D.78
▶ Answer & Explanation

Correct answer: B. 91

This is a combination problem where the order of teams playing does not matter. We need to find the number of ways to choose 2 teams out of 14 to play a match. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items, and r is the number of items to choose. In this case, n=14 and r=2. Therefore, the number of matches is 14C2 = 14! / (2! * 12!) = (14 * 13) / (2 * 1) = 91.

Source: UPSC gs1 2010

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