Mathematics: There are $5$ girls and $5$ boys in a chess club. the club holds a round-robin tournament in which every player plays against every other player exactly once. in how many games does a girl play against another girl?

There are $5$ girls and $5$ boys in a chess club.

Bladedrose2351

31.05.2020

Let's call the five girls $g_1, g_2, g_3, g_4 \text {and } g_5$ .

Since every player plays against every other player exactly once, g_1 has to play against $g_2, g_3, g_4 \text {and } g_5$ . This are four maches.

g_2 has already played against g_1 , so she has to play against $g_3, g_4 \text {and } g_5$ . This are three matches.

g_3 has already played against $g_1 \text{ and } g_2$ , so she has to play against $g_4 \text {and } g_5$ . This are two matches.

g_4 has already played against $g_1, g_2 \text{ and } g_3$ , so she has to play against g_5 . This is one match.

So, the total is 4+3+2+1 = 10 matches.

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Aerial14

06.06.2023

idek

step-by-step explanation:

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