If there are twenty-five people in a room and each person shakes the hand of every person in the room once, how many handshakes will there be (do not count)?
Please help!
2007-10-25 20:29:12 · 8 answers · asked by vindictive_voice 3 in Science & Mathematics ➔ Mathematics
Think about this logically.
The first guy has to shake 24 other people's hands.
The second guy has to shake the first guy (which is already counted) and then 23 more.
The third guy already has two done & must do 22 more
the 24th guy has already shaken the hand of 23 guys & has one more
The last guy doesn't have any more.
So the answer is 1+2+3+. . .+23+24
There is a formula for this -- but you can notice that:
1+24 = 25
2+23 = 25
3+22 = 25
etc
There are 12 pairs that add up to 25 -- so the answer is 12*25 = 300
BTW -- the formula for the sum of numbers from one to n is n*(n+1)/2
Here we get 24*25/2 = 300
2007-10-25 20:40:51 · answer #1 · answered by Ranto 7 · 4⤊ 0⤋
right, u don't shake hands with urself, so let that be the same case for the question
each person shakes every other person in teh room but themselves
so there will be 24 handshakes made by each person
so 25 (the people in the room) x 24 (handshakes each) = 600
answer:
600 handshakes in total!
NO NO NO!!!
each person will have some done already (unless it was the first person who started to shake hands)
logic!
the first person makes 24 handshakes
the next 23
the next 22
so the numbers go down.....
so u need to divide the 600 by 2
cause u would have counted too many handshakes and infact exactly double!
answer: 300 handshakes in total!!!!!!
now that is right
2007-10-25 22:53:10 · answer #2 · answered by Anonymous · 1⤊ 0⤋
25 C 2 is the answer.
Because out of 25 people each time we have to select 2 people for a handshake.
25 C 2 = 25! / (2! *23!) = 300 handshakes.
In general the number of handshakes for n people shaking hands = n C 2 .
2007-10-25 20:52:39 · answer #3 · answered by gauravragtah 4 · 4⤊ 0⤋
300 handshakes, its easy... guy #1 shakes 24 times and sits down, hes done. guy 2 shakes 23 times(everyone left) and sits down. This continues until the final handshake. Basically its 24 + 23 + 22 + 21 ..... + 1 = ??? YOu can do it out, but its easier to think about it like this: 24 + 1 = 25 ok, 23 + 2 = 25 ok 22 + 3 = 25...See where this is going... 13 + 12 = 25....so its 25 times 12 = 300.
2007-10-25 20:49:38 · answer #4 · answered by P F 1 · 0⤊ 0⤋
became the unique situation (8x+6) / 2 = 0 ? Then 8x+6 = 0 8x = -6 x = -(6/8) x = -¾ in case you probably did submit the completed situation, then I trust the different solutions you have won.
2016-12-30 06:16:20 · answer #5 · answered by ? 3 · 0⤊ 0⤋
true but what about when two people shake hands does that count as 2 hand shakes?
i think it is 25 people * 24 - 25 of the same hand shakes(two of the same people). i think that sounds okay
2007-10-25 20:39:45 · answer #6 · answered by Scotty 3 · 0⤊ 4⤋
24x
23x
22x
21x
20x
19x
18x
17x
16x
15x
14x
13x
12x
11x
10x
09x
08x
07x
06x
05x
04x
03x
02x
01x
is it 295? thats what i got
oh the third dude is hecka smart good job!
i was close...
2007-10-25 20:41:12 · answer #7 · answered by Anonymous · 0⤊ 1⤋
have you tried counting?
2007-10-25 20:55:40 · answer #8 · answered by Anonymous · 0⤊ 1⤋