Math, asked by Anonymous, 2 months ago

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

Answers

Answered by Anonymous
22

 {\pmb{\underline{\sf{ Required \ Solution ... }}}} \\

As We know that there are Total 8 teams in a certain league Stage Event.

Each team plays with the other team exactly one match then,

Total Numbers of the Matches played in an Event of Sports as:

 \begin{gathered} \small\boxed{\begin{array}{c|c}  \bigstar{\pmb{\underline{\sf{Teams\ (in\ League)}}}} & \bigstar{\pmb{\underline{\sf{Number\ of\ Matches}}}} _{\sf\gray{(Presented \ by \ @ViralBoi)}} \\ \\ \dfrac{\qquad\qquad}{ \sf Team \ A} &\dfrac{\qquad\qquad}{ \sf 7} & \\ \dfrac{\qquad\qquad}{ \sf Team \ B} &\dfrac{\qquad\qquad}{ \sf 7} & \\ \dfrac{\qquad\qquad}{ \sf Team \ C} &\dfrac{\qquad\qquad}{ \sf 7} & \\ \dfrac{\qquad\qquad}{ \sf Team \ D} &\dfrac{\qquad\qquad}{ \sf 7} & \\ \dfrac{\qquad\qquad}{ \sf Team \ E} &\dfrac{\qquad\qquad}{ \sf 7} & \\ \dfrac{\qquad\qquad}{ \sf Team \ F} &\dfrac{\qquad\qquad}{ \sf 7 } & \\ \dfrac{\qquad\qquad}{ \sf Team \ G} &\dfrac{\qquad\qquad}{ \sf 7 } & \\ \dfrac{\qquad\qquad}{ \sf Team \ H} &\dfrac{\qquad\qquad}{ \sf 7 } & \end{array}} \end{gathered}

» (8 × 7) » 56 Matches

But As We know that Every team Can't play Match lonely or by themselves. They always need second team to play with them.

So, We know that If a single match played then Two teams always participate in that which means 2 teams will play in single match.

 \colon\implies{\sf{ \dfrac{56}{2} }} \\ \\ \colon\implies{\sf{ 28 }}

Hence,

» There are 28 matches played in a certain League consisting of 8 teams.

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