25 people meet at a party. Each person shakes hands with each of the others exactly once. How many handshakes are exchanged?
2007-01-16 02:19:07 · 16 answers · asked by Arthur Q 3 in Science & Mathematics ➔ Mathematics
Is the answer 300 handshakes?
The 1st person can shake hands with 24 people.
The 2nd person can make 23 unique handshakes (24 people in the room - 1st person whose hand he already shook).
The 3rd person can make 22 unique handshakes.
So the answer should be adding 24+23+22+21+...1.
Or, a shortcut for this calculation would be to notice that sum of the end numbers equals 25 (24+1 = 25). The sum of the next two end numbers also equals 25 (23+2). The two middle numbers are 12 & 13, which also sums to 25. So:
25*12 = 300 handshakes
2007-01-16 02:29:34 · answer #1 · answered by ybdogsct 2 · 0⤊ 0⤋
The interaction (handshake) would be between two people, avoiding repititions the number of handshakes can be computed by 25C2 = 25! / 23!2! = 24*25 / 2 = 12 * 25 = 300.
The process involves the same thing other answerers have presented.
2007-01-16 11:11:52 · answer #2 · answered by yasiru89 6 · 0⤊ 0⤋
Each person is supposed to shake 24 hands.
Each person shakes every other person's hand.
24+23+22+21+...+2+1 = 25*24/2 = 300
2007-01-16 10:32:46 · answer #3 · answered by mipsaction 1 · 0⤊ 0⤋
The first person shakes hands with 24 people.
The second person shakes hands with 23 other people.
The third person shakes hands with 22 other people.
...
So 24 + 23 + 22 + 21 + 20 + ... + 1 = 25 * 24/2 = 300
2007-01-16 10:27:25 · answer #4 · answered by anton3s 3 · 0⤊ 0⤋
300. Each person shakes 24 other people's hands. The first guy shakes hands with 24 other people. The second guy only gets 23 of his handshakes counted, since he shook hands with the first guy and it was already added. The third guy counts 22 since he shook hands with the first and second guy, and so on down the line.
24+23+22+21+.....3+2+1=300
2007-01-16 10:26:17 · answer #5 · answered by theeconomicsguy 5 · 1⤊ 0⤋
The answer is 24*25/2=300
Kids way: First person hs with 24, within 24 second person hs with 23 and so on...total number of hs 1+2+...+24=24(24+1)/2
Grown ups: Combinations of 2 from 25=25C2=300
2007-01-16 10:31:28 · answer #6 · answered by Defunct 2 · 1⤊ 1⤋
Each person shakes 24 hands, so it would be 25*24=600... except that you would be double-counting so the answer is half that number.
By the way, it's 300... not "300 hundred".
2007-01-16 10:35:01 · answer #7 · answered by Anonymous · 0⤊ 0⤋
50
2007-01-16 10:49:58 · answer #8 · answered by richardsmith582000 1 · 0⤊ 0⤋
How many possible combinations? 25 times 25=625 handshakes :)
2007-01-16 10:28:54 · answer #9 · answered by true blue 6 · 0⤊ 1⤋
600.... each person shakes hands with only 24 other people.. there are 25 people at the party.. so 24x25 = 600.
2007-01-16 10:33:53 · answer #10 · answered by Anonymous · 0⤊ 1⤋