Question

At a business meeting of five people, every person shakes hands with every other person one time. How many total handshakes occur

Answer 1

$\huge{\red{\boxed{\underline{\overline{\mathbb{\pink{Solution}}}}}}}$

$\mathfrak\blue{answer}$

10 handshakes will be there .

$\mathfrak \blue{given}$

—☆There are 5 people.

—☆Each will shake hand once .

$\mathfrak \blue{to \: find}$

—☆ Total number of handshakes .

$\mathfrak \blue{1st \: method}$

Let the five people as A , B , C , D , E

—☆ Now A will shake hand with B , C, D, E.

—☆ B will shake hand with C , D, E ( As he has already done with A ) .

—☆ C will shake hand with D and E .

—☆ D will shake hand with E .

—☆ E has no need to shake hand as everyone has did .

So total number of hand shakes is 4 + 3 + 2 + 1

→ 10 times

$\mathfrak \blue{2nd \: method}$

—☆In this type of questions we use a formula that is

$\mathfrak \blue{a \: = \frac{n(n - 1)}{2}}$

$a = \frac{5(5 - 1)}{2}$

$a = \frac{5 \times 4}{2}$

$a = {5 \times 2}$

$a = 10$

So , answer is 10 times .