[Math help] If there are 6 people in a room, and each person shakes hands with everyone else exactly once, ...

how many handshakes are there?

a) 6
b) 15
c) 30
d) 12
e) 18

Can you please explain as well? Best answer will be chosen.

A will shake hands with B C D E F
B will then shake hands with C D E F
C will then shake hands with D E F
D will then shake hands with E F
E will then shake hands with F


15

The answer is b, 15.

Person 1: shakes hands with 5 people
Person 2: shakes hands with 4 people
Person 3: shakes hands with 3 people
Person 4: shakes hands with 2 people
Person 5: shakes hands with 1 person
Person 6: shakes hands with no one because he has already shaken everyones hands

You would then add up 5, 4, 3, 2, and 1 to get a total of 15.

*an easier way is to just the number of people and subtract by one and then add the rest of numbers*
EX: There are 9 people in the room, blah blah blah...
You would add 8 plus 7 plus 6 plus 5 plus 4 plus 3 plus 2 plus 1...and get your answer
EX: There are 23 people in the room, blah blah blah...
You would add 22 plus 21 plus 20 plus 19 plus 18...so on and so forth.

B
first person will shake hand with five person
Second person will shake hand with four person(he can't shake hand again with first person, cause it said exactly once)
Third person will sake hand with three person(he can't shake hand again with first and second person)
Fourth person will shake hand with two person(can't shake hand again with first, second and third person)
Fifth person will shake hand with one person(can't shake hand with first, second, third and fourth person)
sixth person already shaked hands with every one.
5+4+3+2+1=15

C.) 30 because 1 person shakes hand with 5 people. So 6 people shakes it 6*5=30 times .

n(n-1)/2=
6(5)/2 = 15

720