number of handshakes?

Question

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

i have two solution in my head i think ...i am not sure though

(a) 10C2

(b)9*9*....10 times =10*9

i dont know who is correct ?

whats the solution ?

Answer 1

(a) is correct.

Each handshake is counted by two different people. If you add up the number of handshakes that each person would report (9 handshakes * 10 people reporting = 90 total)... you'd count A reporting his handshake with B, and B also reporting the same handshake with A.

Since method (b) counts each handshake twice, you have to divide by two, which yields the same result as (a). (Note that I'm assuming you meant "9+9+9+9..." for (b), and not "times".)

It's 10*9/2 = 45

Answer 2

9+8+7+6+5+4+3+2+1=45 handshakes

Answer 3

You need to understand that the first person will shake hands with 9 people. The second person already shook hands with the first. So he will shake hands only 8 more times. The third with 7 and so on. Until; the last person who will have already shaken hands with the other 9 people.
So
9+8+7+6+5+4+3+2+1+0=45

Answer 4

10C2

Three ways to motivate:

- Out of 10 people, you choose two to shake hands, and since it's the same handshake regardless of which order you chose them in, so use combinations rather than permutations. So 10C2.

- Alternately: Choose the first shaker (10 choices), choose the second shaker (9 remaining choices), and divide by two since it doesn't matter who was chosen first. So (10*9)/2.

- 10C2 is equal to (it turns out) 9+8+...+1. (The sum from 1..n is n(n+1)/2; when n=9 you can see that this is 10*9/2.)


P.S. Thanks for hazarding your own hunches; it's more annoying when people are trying to get homework answers but not putting forth any effort themselves.

Answer 5

9+8+7+6+5+4+3+2+1=45

54 handshakes in all.
there are 10 people
1 will shake the 9 hands
next 1 will shake 8
next 7
next 6
nxt 5
nxt 4
nxt 3
nxt 2
nxt 1
last will shake no hands.
definitely (a)

Answer 6

If it was (b), everyone would be dead before they'd finished shaking hands.

The answer is 10*9/2, since each of the 10 people shakes hands with 9 others, and each handshake involves 2 people.

So, 45.
.

Answer 7

There are 10 persons... as the 1st person will shake hands with the remaining 9 persons...the remaing 9 will not shake hands with the same person again... and the last person will not shake hands with himself......so it goes like....
9+8+7+6+5+4+3+2 = 44

Answer 8

54

Answer 9

90 handshakes + 1 at home.

Answer 10

Back in the old school ten time ten was 100