7 people take part in a panel discussion. Each person is to shake hands with all of the other participants at the beginning of the discussion. How many handshakes take place? List them all.
i just don't know that rate of this problem. Can somebody help me?
2007-03-10 15:46:40 · 3 answers · asked by Ha!! 2 in Science & Mathematics ➔ Mathematics
There are 7!/(2!5!) = 21 handshakes. It's the number of ways that you can select 2 people from a group of 7. Let's name the people A, B, C, D, E, F, and G. Here is a list of the possible hand shakes.
1. AB
2. AC
3. AD
4. AE
5. AF
6. AG
7. BC
8. BD
9. BE
10. BF
11. BG
12. CD
13. CE
14. CF
15. CG
16. DE
17. DF
18. DG
19. EF
20. EG
21. FG
2007-03-10 15:52:16 · answer #1 · answered by blahb31 6 · 1⤊ 0⤋
Single person handshakes with 6 others. Since there are 7 persons there will be 7*6 = 42 handshakes. However that includes double handshakes (i.e. I handshake with you and you handshake with me). Therefore number of different handshakes is 7*6/2 = 21. Generally for n persons number of handshakes will be n*(n-1)/2.
2007-03-10 23:56:20 · answer #2 · answered by fernando_007 6 · 0⤊ 0⤋
the rate is 2 because two peole shake hands.
nCr = n! / ((n-r)! * r!)
7C2 = 7! / ((7-2)!*2!) = 21 handshakes
2007-03-10 23:50:41 · answer #3 · answered by 7 · 1⤊ 0⤋