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Question

Mathematics Question on permutations and combinations

If one person handshakes with the other only once and number of handshakes is 6666, then number of persons will be

A

10

B

33

C

24

D

12

Answer

12

Explanation

Solution

Let the total number of persons be nn. ∴ nC2=66\therefore \,^{n}C_{2}=66 ⇒n(n−1)2=66\Rightarrow\frac{n\left(n-1\right)}{2}=66 ⇒n2−n−132=0\Rightarrow n^{2}-n-132=0 ⇒(n−12)(n+11)=0\Rightarrow\left(n-12\right)\left(n+11\right)=0 ⇒n=12(∵n≠−11)\Rightarrow n=12 \left(\because n\ne-11\right)