How many handshakes take place?

Question

Two ten member basketball teams play a game. After the game, each of the members of the winning team shakes hands once with each member of both teams. How many handshakes take place? The answer should be 145 but I don't know how I get it. Please help. Thank you.

Answer 1

Break it into two parts. First, the winners shake hands with the losers. That's 10 people shaking the hands of each of another 10 people. 10 times 10 is 100.

Next is the winners shaking hands with their own team. The first guy shakes the hand of 9 people. The second guy shakes hands with 9 people too, but he's already shaken hands with the first guy, so don't count that twice. The third guy shakes 9 guys' hands, but you've already counted the first two--that means 7 more. Keep this up, and you get:

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

The 10th guy has already been counted for every person. So that sums up to 45.

Add 100 and 45 = 145. Done!

Answer 2

Break the problem into two parts.

First, the winning team shakes hands with each player on the losing team. Thus, each player on the winning team has 10 handshakes; there are a total of 100 such handshakes.

Second, the winning team shakes hands with its own players. Each of the 10 shakes 9 other players' hands AND each of those handshakes could mistakenly be counted twice - once per player. So, in actuality ther are (10 x 9)/2 = 45 of these kinds of handshakes.

All told, there are 100 + 45 = 145 handshakes.

Answer 3

There are 100 hand shakes between the teams. 10 X 10 = 100 every member (10) of the team MUST shake 10 of the other team memebers. Then after that they must shake their own team (but inly the winning team, losers do not shake anymore).. here there will be 9 X 10, but only half of these will count, because they are counted twice.. as each person (10) shakes 9 peoples hands. BUT BOb shaking Jo is the same as Jo shaking Bob... so 9X10 / 2 = 45. 100 +45 = 145

Answer 4

1st player shakes hands with 19 players
2nd player shakes hands with 18 players
3rd player shakes hands with 17 players
...
10th player shakes hands with 10 players

Total = 19+18+17+...+10 = 145

or,
19+18+17+...+10 = (19+18+17+...+1) - (9+...+1)

= 19(19+1)/2 - 9(9+1)/2 = 190 - 45 = 145

Answer 5

Well, each each player shakes hands with 19 people.

So 19 * 20 is if you count every handshake twice.

So the answer is 190

Answer 6

The elementary way is you let A, B, C...J be the members of team #1 and a, b, c...j members of team #2. Get one from each team and pair it with another member. But be careful that Aa is the same as aA so count this as one If you complete the list correctly, you should get 190.

Another way is by combination.
nCr = n!/[(n-r)!(r!)]

20C2 = 20!/[(20-2)!2!]

= 190

Answer 7

alright....... 1111111111 (10 handshakes or 20 handshakes)
1111111111

1111111111 (9 handshakes or 19 handshakes)
1111111111

1111111111 (8 or 18
1111111111

so on like this moving the *1's (players) down as they shake hands.....

if one handshake between 2 players actually equals two because each individual is counting his own handshakes, then your answer is not 145 it is 165.

if one handshake between 2 players in only counted as one handshake....then the answer is not 145 it is 124

Answer 8

it dosent matter....

its just math