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
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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Notes on permutations and combinations
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.