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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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?

Usamah Prosser · Accepted Answer

Step 1&amp;nbsp;The total number of people&amp;nbsp;=6.&amp;nbsp;They greet each other at a meeting by shaking hands with one another&amp;nbsp;We have to find the total number of handshakes.&amp;nbsp;Step 2&amp;nbsp;Make a plan.Each handshake requires a group of two persons.And then we have to find the total number of groups.&amp;nbsp;Step 3&amp;nbsp;Implement the strategyWe can choose a group of 2 people from 6 people&amp;nbsp;6C2=6!2!(6−2)!=15&amp;nbsp;ways.&amp;nbsp;Step 4&amp;nbsp;Each person will handshake with 5 people. So&amp;nbsp;(6×5)=30, but when two people handshake then it is the same event.&amp;nbsp;In these 30 cases, we have repetitions. Each case occurred twice. So the total number of cases&amp;nbsp;=302=15&amp;nbsp;The issue is resolved by this.Result: 15

Accepted Answer

A1=6 A3=24

Andre BalkonE · Accepted Answer

To solve this problem, we can use the combination formula to determine the number of handshakes that take place.The combination formula, denoted as (nr), calculates the number of ways to choose a group of r objects from a larger set of n objects, without regard to the order of selection.In this case, there are 6 people who greet each other by shaking hands. To determine the number of handshakes, we need to choose 2 people at a time to shake hands. Therefore, n=6 and r=2.Using the combination formula, we have:(62)=6!2!(6−2)!Simplifying this expression, we have:(62)=6·5·4!2·1·4!Cancelling out the factorials, we get:(62)=6·52·1Evaluating the multiplication, we have:(62)=302Simplifying the division, we find:(62)=15Therefore, there are 15 handshakes that take place when six people greet each other at a meeting.

xleb123 · Accepted Answer

Step 1: Understand the problem.The problem states that six people greet each other at a meeting by shaking hands with one another. We need to determine how many handshakes take place in total.Step 2: Devise a plan.To solve this problem, we can use the concept of combinations. Each handshake involves two people, so we need to find the number of ways we can choose 2 people out of 6.Step 3: Carry out the plan.The formula for combinations, denoted as (nk), represents the number of ways to choose k items from a set of n distinct items without regard to the order. In this case, we want to find (62), which will give us the number of handshakes.The formula for combinations is given by:(nk)=n!k!(n−k)!Substituting n = 6 and k = 2 into the formula, we have:(62)=6!2!(6−2)!Simplifying further:(62)=6!2!4!Step 4: Look back and check.Let&#039;s evaluate the expression (62) using the factorial notation:(62)=6×5×4×3×2×12×1×4×3×2×1Canceling out the common terms:(62)=6×52×1=302=15So, there are 15 handshakes that take place when six people greet each other at a meeting.In conclusion, there are (62)=15 handshakes that take place at the meeting.

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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