Question:
If one person handshakes with the other only once and number of handshakes is $66$, then number of persons will be
If one person handshakes with the other only once and number of handshakes is $66$, then number of persons will be
Updated On: Jul 6, 2022
- 10
- 33
- 24
- 12
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The Correct Option is D
Solution and Explanation
Let the total number of persons be $n$.
$\therefore \,^{n}C_{2}=66$
$\Rightarrow\frac{n\left(n-1\right)}{2}=66$
$\Rightarrow n^{2}-n-132=0$
$\Rightarrow\left(n-12\right)\left(n+11\right)=0$
$\Rightarrow n=12 \left(\because n\ne-11\right)$
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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.