word problem question?

Question

alright I know this is an easy question...but I'm stupid

Fourteen students in P's class were asked to shake hands with each other. Each student shook hands with each of the other students exactly once. How many handshakes occurres in Ms. Power's class?

-I got 90... is that right?

Answer 1

The answer is 91. Where was your mistake? I have no idea but to make the solution simple, draw a simple diagram designating each student like this:


1 2 3 4 5 6 7 8 9 10 11 12 13 14

Start with student no. 1. How many hands does he/she shake? 13, right? All the 13 students on his/her right side as shown in our diagram above.
Next, student no. 2. How many hands does he/she shake on her right side? 12, right? Why not 13? Because he/she had shaken hands with student no. 1 who is on his/her left side. So it's 13-1 or 12.
Next, student no. 3. How many hands does he/she shake?
11, right? Why not 13? Because he/she had shaken hands with student no. 1 and 2, who are both on his/her left side. So it's 13-2 or 11.
We can say now that student no. 4 will shake 13-3 hands or 10, the 3 being the number of students on his/her left side.Etc, etc. ........Student no. 13 will shake 13-12 or 1. Student no. 14 will shake no one's hand. Poor he/she...but wait! he/she had actually shaken hands with the rest of the 14. Only that on his/her turn in our diagram there was no one else on his/her right to shake hands with.

Now write down the student numbers again and opposite each student number write down the number of hands shaken by each on his/her right side, thus:

1 2 3 4 5 6 7 8 9 10 11 12 13 14

13 12 11 10 9 8 7 6 5 4 3 2 1 0.

Add all the above numbers and you get 91.

I'm just like you, but to make my life easier in solving math problems, I often resort to diagrams to visualize what needs to be done to solve the problem.

Answer 2

13+12+11+10+9+8+7+6+5+4+3+2+1= 91

Answer 3

Considering the hand-shake with 1 person only once
1st student shakes 13 hands.
2nd student shakes 12 hands.
.......
13th student shakes 1 hand.

So number of handshakes = 13+12+11+10+...+4+3+2+1 = 91

Answer 4

I got 91
the first guy shakes the other 13 guys hand so he doesn't have to shake anyone else's hand. I counted it like this
13+12+11+10+9+8+7+6+5+4+3+2+1= 91
you're not stupid baby girl...never think that about yourself!

Answer 5

Hi, you are all making it sound complicated. Don't need complicated formulas to solve this. Look at it this way.
Each student will shake with 13 students, right?
So 14 students would shave shook 13x14=182, correct?
Now because 2 shakes make a handshake, you divide 182/2....so the answer is 91.
And no, this is not really an easy question and you are not stupid. Just 'cos you are not good in numbers does not make you stupid. Also we can be all stupid sometimes..even Einstein admits that.
Now if you want to thank me, pick me as best answer :)

Answer 6

Handshakes involve pairings.

How many combinations of 14 students can you get 2 at a time.

(n,k) = n!/[k!(n-k)!]
(14,2) = 14!/[2!(12!)]

14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
--------------------------------------------------------------------
2 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2

(14 x 13)/2 = 7 x 13 = 91

You missed one.

Answer 7

14 people each shake 13 other peoples hands (14x13), but that counts every handshake twice (once for each participant) so the answer is (14x13)/2 = 91

Answer 8

I'm not sure but I think the answer is 13+12+11+10+9+8+7+6+5+4+3+2= 90

so i think u r right

Answer 9

What shapes do you get once you chop up the sq. with a diagonal? 2 trangles. because of the fact all of us recognize the sphere is a sq., meaning each and all of the aspects are equivalent (for this reason, in case you recognize one factor, you recognize each and all of the aspects). So now you have a trangle with 2 aspects equivalent to 60 feet. you may now use Pythagorean's theorem: A (squared) + B(squared) = C (squared) A and B are your 2 aspects after which you basically clean up for C. solid success!

Answer 10

Well if you start with 14 & it takes 2 to shake & they all only shook once that's 7 pairs of people shaking hands.

;-)