Question

after a meeting ended , all the members of the meeting shake hands with each other . if there were 190 handshakes made in that room after that meeting , how many total people were present in the room ?
options -:
a. 19
b. 10
c. 20
d. 15
please provide the answer with complete explanation . wrong answers will be reported immediately . ..............
♡ katyayni121 ♡ ​

Answer 1

Answer:

option c) 20

let the number of persons be n

two persons will shake hands. hence total number of handshakes will be equal to the total number of ways of selecting two persons out of the n persons. the number of ways is equal to nC2, hence

nC2 = 190

n!/(n-2)!*2! = 190

n*(n-1)/2 = 190

n(n-1) = 190*2

n^2 - n - 380 = 0

n^2 - 20n + 19n - 380 = 0

n(n-20) + 19(n-20) = 0

(n-20)(n+19) = 0

n = 20, -19

n cannot be negative.

hence n = 20

Answer 2

Answer:

c. 20 is answer dear friend