Question

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✌️Here is a tricky maths question for you....let's se who has guts to solve this....☺️


✍️At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

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Answer 1

$\huge{\mathfrak{Question:-}}$

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

$\huge{\mathfrak{Answer:-}}$

Let the total person in the party be n.

As hand shakes occurs between 2 persons, so we need to select any two people out of n.

This can be done in

$\sf{^{n}C_{2}}$

ways

Given, total number of hand shakes = 66

$\sf{\implies ^{n}C_{2}=66}$

$\sf{\implies \frac{n}{2(n-2)}=66}$

$\sf{\implies \frac{n(n-1)(n-2)}{2(n-1)}=66}$

$\sf{\implies \frac{n(n-1)}{2}=66}$

$\sf{\implies n(n-1) = 132}$

$\sf{\implies n^{2}-n-132=0}$

$\sf{\implies n^{2} -12n+11n-132=0}$

$\sf{\implies n(n-12)+11(n-12)=0}$

$\sf{\implies (n+11)\;(n-12)=0}$

$\sf{\implies n = -11\;or\;n=12}$

As total number of persons cannot be negative, so $\sf{n \neq -11.}$

$\sf{\therefore n = 12}$

$\boxed{\sf{Hence,\;total\;number\;of\;persons=12}}$

Answer 2

Answer:

The formula for the number of handshakes possible at a party with n people is

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.# handshakes = 10*(10 - 1)/2.

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.# handshakes = 10*(10 - 1)/2.# handshakes = 10*(9)/2.

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.# handshakes = 10*(10 - 1)/2.# handshakes = 10*(9)/2.# handshakes = 90/2.

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.# handshakes = 10*(10 - 1)/2.# handshakes = 10*(9)/2.# handshakes = 90/2.# handshakes = 45

The formula for the number of handshakes possible at a party with n people is# handshakes = n*(n - 1)/2.This is because each of the n people can shake hands with n - 1 people (they would not shake their own hand), and the handshake between two people is not counted twice.This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.# handshakes = 10*(10 - 1)/2.# handshakes = 10*(9)/2.# handshakes = 90/2.# handshakes = 45So, there are 45 handshakes that can be made between 10 people.