Question

A rugby tournament with 10 teams is organised. Each team will play each other exactly once. Work out the total number of games played.

Answer 1

45

Explanation:

Answer 2

45

Explanation:

Total no. of teams = 10

1 game will be played between no. of teams = 2

We are supposed to find the total number of games played if Each team will play each other exactly once.

We will use combination

Formula :
`^nC_r =(n!)/(r!(n-r)!)`

n = 10

r = 2

`^(10)C_2 =(10!)/(2!(10-2)!)`

`^(10)C_2 =(10!)/(2!(8)!)`

`^(10)C_2 =(10 * 9 * 8!)/(2!(8)!)`

`^(10)C_2 =(10 * 9)/(2 * 1)`

`^(10)C_2 =45`

Hence the total number of games played are 45