Question

In a class of 20 students, how many conversations must be had so that every student talks to every other student in the class?

A) 190
B) 380
C) 760
D) 6840

Answer 1

`\text{A) }190`

Explanation:

Similar to the handshake problem, if every student must talk with another person, each student will talk to 19 other students. However, a conversation consists of two people, so we must divide the number of ways we can rearrange the two people (
`2!`). Therefore, our answer is
`(20\cdot 19)/(2!)=\boxed{\text{A) }190}`

Answer 2

The answer is b - 380 students because each student (20 total) has to talk to 19 other students. 20*19= 380