New Year Party

Probability Level 1

In the new year party,there were 10 persons and each person handshaked with every other person.Calculate the no. of handshakes?

Note: each person handshakes with every other person only once


The answer is 45.

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Aakash Jain by Aakash Jain , 23, India

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4 solutions

Denel Joi
Jul 5, 2014

Say there are n people. The first person shakes his hand with the other n-1 people. The second person then shakes his hand with the other n-2 people, and so on until the (n-1)th person shakes his hand with the nth person.

So the number of handshakes is (n-1) + (n-2)... + 3 + 2 + 1 which equals (n-1)(n)/2.

(10*9)/2 So, 90/2 = 45

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this is like how many ways to take 2 person from 10 person so C(10,2)

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Pankaj Nirwan
Jul 15, 2014

we all know very popular formula i.e n(n-1)/2 For This given problem we use above formula to solve it let n = 10 ( In new year party,there were 10 persons ) so ; n(n-1)/2 = 10(10 -1)/2 = 10 x 9 /2 = 90/2 = 45

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The first person shake the hand of 9 people. The 2nd shake the hand of 8 people, the 3rd person shake the hand of 7 people and so on. In the end we have 9+8+7+6+5+4+3+2+1 handshakes. Answer: 45

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