Suppose you are organizing a business meeting and are in charge of facilitating

Question

Suppose you are organizing a business meeting and are in charge of facilitating the introductions. 1.How would you arrange a group of n people so each person can shake hands with every other person? 2. How might you organize this process? 3. How many times will each person shake hands with someone else? 4. How many handshakes will occur? This answer should be expressed as a general counting formula that depends on the value of n. It may be easier to see how you might want to solve this by first working with specific (small) values for n, such as 5 or 6, before trying to address the general problem.

Explanation / Answer

Let us consider n people.

Select one person from n.

Then he can shake with remaining n-1 persons.

The first person selected is set aside.

Now from the remaining n-1 persons 1 person is taken and he is asked to shake hand with remaining n-2 persons.

Then the second person now will join the first person.

This process is repeated until last two. They complete and go.

Now each person in the party has completed hand shake with each other.

There are totally n-1, n-2, n-3,......,1

Total no of handshakes = sum of n-1 natural numbers

Whether n is odd or even the answer is the same as above.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.