Everyone has a telephone (pop. 84), how many 2 way convo's can take place?

Question

I thought it might be 32 but i'm still a little fuzzy! Help!

i thought it was 42 not 32*

Answer 1

Look at it this way. The first person can call 83 other people. The second person does not need to call the first person; they already had a conversation. So the second person can only call 82 people. Continuing on, the 82nd person only needs to call one person: the 83rd person; all of the first 81 people have already called him or her. And the 83rd person calls nobody, because everybody already called him or her. So the result is 83 + 82 + 81 + ... + 2 + 1. There is a trick to summing up numbers 1 through n. The sum is (n + 1)*n/2. So this sum would be 84*83/2 = 3486 two-way phone calls.

Answer 2

If it is at the same time
84/2 = 42

If at different times
(combination of 84, two at a time)
= 84 x 83 / (1x2)
= 42 x 83
= 3486

Answer 3

It takes two people to make a two way conversation. Therefore, you need to divide 84 by 2, which will give you 42.