38
Everyone shakes hands with 4 other people. Since there are 5 people in the room this would suggest there are 5*4 = 20 handshakes. However, you would then be double counting handshakes: A shaking hands with B and B shaking hands with A is, in reality, only one handshake. Thus there are 5*4/2 = 10 handshakes in all.
There will be 28 handshakes. If you ask each person how many handshakes they had they will tell you 7 making 7 x 8 = 56 handshakes in all. But every hand involves two people, so every handshake has been counted twice, thus there are 56 / 2 = 28 handshakes in all.
3. AB, BC and CA.
Ah, what a lovely thought! When each person shakes hands with every other person at the party, it creates a beautiful connection. In this case, with 3 people at the party, there will be 3 handshakes in total. Just imagine the joy and warmth shared in those simple gestures!
190
Sixty-six unique, distinct handshakes.
So, there will be 3 handshakes among the 3 people at the party.
Everyone shakes hands with 4 other people. Since there are 5 people in the room this would suggest there are 5*4 = 20 handshakes. However, you would then be double counting handshakes: A shaking hands with B and B shaking hands with A is, in reality, only one handshake. Thus there are 5*4/2 = 10 handshakes in all.
There will be 28 handshakes. If you ask each person how many handshakes they had they will tell you 7 making 7 x 8 = 56 handshakes in all. But every hand involves two people, so every handshake has been counted twice, thus there are 56 / 2 = 28 handshakes in all.
15
You could never guarantee 1000 handshakes because the people may choose not to shake hands! If each person did shake hands with everyone else, then 46 people would suffice.
3. AB, BC and CA.
Ah, what a lovely thought! When each person shakes hands with every other person at the party, it creates a beautiful connection. In this case, with 3 people at the party, there will be 3 handshakes in total. Just imagine the joy and warmth shared in those simple gestures!
15 (15 * 15 - 15)/2 = 105
if there are 2 people in a room and each one shakes hands once with every other person in the room, how many hand shakes are there?... answer( 1 handshake) pretty easy isn't it? if there are 3 people in a room and everyone shakes hands with everyone else, how many hand shakes are there? answer( three handshakes) now how many handshakes will there be for 5 people in a room? its your time to shyne...
The first person must shake hands with 5 other people. The next must shake hands with 4 other people, since you exclude the first person. Keep going and you'll find that there will be 5+4+3+2+1=15 handshakes. Numbers like this are called triangular numbers.
190