Question:
There are $12$ points in a plane. The number of straight lines joining any two of them, when $3$ of them are collinear, is
There are $12$ points in a plane. The number of straight lines joining any two of them, when $3$ of them are collinear, is
Updated On: Jun 23, 2024
- $ 60 $
- $ 63 $
- $ 64 $
- $ 65 $
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The Correct Option is B
Solution and Explanation
Required number ways $ {{=}^{12}}{{C}_{2}}{{-}^{3}}{{C}_{1}} $
$ =\frac{12\times 11}{1\times 2}-3 $
$ =6\times 11-3 $
$ =66-3=63 $
$ =\frac{12\times 11}{1\times 2}-3 $
$ =6\times 11-3 $
$ =66-3=63 $
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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.