Question

In how many ways these n people can make handshakes so that no two handshakes crosses each other. N would be even.

Answer 1

Answer:

See every people will do handshake with 1 of his hand and so total handshakes that took place   we can simply use this formula n(n-1)/2 as the no of handshakes are in AP where n = no.of persons

so 91 x 2  =  n² - n 

⇒ n² - n - 182 = 0

⇒n² - 14n + 13n - 182 = 0

⇒ n(n - 14) + 13(n - 14) = 0

⇒(n - 14)(n + 13) = 0

so n = -13 or 14 so no. of persons can't be negative so no of persons is 14  ANSWER