# Solve the following problems applying Polya’s Four-Step Problem-Solving strategy. If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
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Usamah Prosser
Step 1
Step 1: Understand the problem
The total number of people $=6.$
They greet each other at a meeting by shaking hands with one another
We have to find the total number of handshakes.
Step 2
Devise a plan
We have to take a group of 2 people for each hand shake.
And then we have to find the total number of groups.
Step 3
Carry out the plan
We can choose a group of 2 people from 6 people $6C2=\frac{6!}{2!\left(6-2\right)!}=15$ ways.
Step 4
Look back(check and interpret)
Each person will handshake with 5 people. So $\left(6×5\right)=30$, but when two people handshake then it is the same event.
In these 30 cases, we have repetitions. Each case occurred twice. So the total number of cases $=\frac{30}{2}=15$
This satisfies the problem.