Question

Five people meet for the first time and shake each other's hand once.



Determine the number of handshakes.

Answer options with 5 options
A.
5

B.
10

C.
15

D.
20

E.
120

Answer 1

To determine the number of handshakes between five people, we can use the combinatorial formula for selecting 2 people from a group of \(n\) people, which is given by:

\[
\text{Handshakes} = \binom{n}{2} = \frac{n(n-1)}{2}
\]

In this case, \(n = 5\):

\[
\text{Handshakes} = \binom{5}{2} = \frac{5 \times 4}{2} = \frac{20}{2} = 10
\]

So, the total number of handshakes is **10**.

Therefore, the answer is **B. 10**.