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5 people enter a racquetball tournament in which each person must play evert other person exactly once. Determine the total number of games that will be played

Respuesta :

mathmate
This is the "handshake problem", namely with n people, how many handshakes will there be if every will shake hands with everyone else.
n people will shake hands with (n-1) other people.  Since we are counting twice for each handshake, the number of handshakes is n(n-1)/2.
For n=5, the number of matches is 5(5-1)/2=10.
This is also the number of diagonals in an n-sided convex polygon.

Answer:

The total number of games that will be played is 10.

Step-by-step explanation:

Consider the provided information.

There are 5 people and each person must play evert other person exactly once.

Each time 2 team will play together out of 5.

It is all possible pairings of the 5 players or 5 objects taken 2 at a time.

So we can solve it as:

[tex]\frac{5!}{2!(5-2)!} =\frac{5!}{2!3!} \\\frac{4\times 5}{2}=10[/tex]

Hence, the total number of games that will be played is 10.

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