Question:
Out of 18 points in a plane, no three are in the same st. line except five points which are collinear. The number of straight lines that can be formed joining them is
Out of 18 points in a plane, no three are in the same st. line except five points which are collinear. The number of straight lines that can be formed joining them is
Updated On: Jul 6, 2022
- 143
- 144
- 153
- none of these.
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The Correct Option is B
Solution and Explanation
Reqd. number of st. lines
$=^{18}C_{2}-^{5}C_{2}+1=\frac{18\times17}{12}-\frac{5\times4}{2}+1$
$=153-10+1$
$=144$
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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.