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anonymous

  • one year ago

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?

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  1. ganeshie8
    • one year ago
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    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.

  2. ganeshie8
    • one year ago
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    That means we end up solving a quadratic equation \[\dfrac{n(n-1)}{2} = 105\]

  3. anonymous
    • one year ago
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    hello

  4. anonymous
    • one year ago
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    i have also got another method,simply we will apply combination NC2 \[N!/2 !(N-2) !=105\]

  5. anonymous
    • one year ago
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    anyhow thanks for the help!

  6. ganeshie8
    • one year ago
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    Yes I like your method

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