Answer:
45
Step-by-step 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 : [tex]^nC_r =\frac{n!}{r!(n-r)!}[/tex]
n = 10
r = 2
[tex]^{10}C_2 =\frac{10!}{2!(10-2)!}[/tex]
[tex]^{10}C_2 =\frac{10!}{2!(8)!}[/tex]
[tex]^{10}C_2 =\frac{10 \times 9 \times 8!}{2!(8)!}[/tex]
[tex]^{10}C_2 =\frac{10 \times 9}{2 \times 1}[/tex]
[tex]^{10}C_2 =45[/tex]
Hence the total number of games played are 45
