Question

There are 4 representatives from each of 4 companies at a convention. At the start of the convention, every person shakes hands once with every person except the other representatives from their company. How many handshakes are there?

Answer 1

All 16 people shake hands with 12 other people (everyone except themselves and the other representatives from their company). In multiplying 16 x 12, each handshake is counted twice, so we divide by two to get the answer of (16 x 12)/2 = 96 handshakes.

Answer 2

Answer: 96 ways

Explanation: this is a combination.

If the company reps are designated as A, B, C & D.

A can have Handshakes with the rest 3

B can have Handshakes with the rest 2

C can shake hands with D

So 3+2+1=6 multiplied by the total number of reps i.e 16.

So 16x6=96