anonymous
  • anonymous
In a party every person shakes hand with every other person. If there was a total 105 handshakes in the party. Find the number of people present who were present in the party?
Mathematics
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anonymous
  • anonymous
In a party every person shakes hand with every other person. If there was a total 105 handshakes in the party. Find the number of people present who were present in the party?
Mathematics
jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
Say there are \(n\) people in the room. The first person may shake hands with \(n-1\) other people. The next person may shake hand with \(n-2\) other people, not counting the first person again. ... Adding them up gives \[(n-1)+(n-2)+\cdots+3+2+1\] which is same as the sum of first \(n-1\) natural numbers.
ganeshie8
  • ganeshie8
That means we end up solving a quadratic equation \[\dfrac{n(n-1)}{2} = 105\]
anonymous
  • anonymous
hello

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anonymous
  • anonymous
i have also got another method,simply we will apply combination NC2 \[N!/2 !(N-2) !=105\]
anonymous
  • anonymous
anyhow thanks for the help!
ganeshie8
  • ganeshie8
Yes I like your method

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