Question:

There are $15$ points in a plane, no three of which are in a straight line, except $6$, all of which are in a st. line. The number of st. lines which can be drawn by joining them is

Updated On: Jul 7, 2022
  • $^{15}C_2-6 $
  • $^{15}C_2-\,^6C_2 $
  • $^{15}C_2-\,^6C_2-1 $
  • $^{15}C_2-\,^6C_2+1 $
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The Correct Option is D

Solution and Explanation

Reqd. no. of st. lines $= ^{15}C_{2}-\,^{6}C_{2}+1$ [$\because$ join of two pts. from a st. line and $6$ pts. which are collinear given only st. line in place of $^{6}c_{2}$]
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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.