its 8C2
that means
[(Factorial 8)] / [ (Factorial 2)(Factorial 6) ]
added OG tag

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This is just applying the idea of choosing combinations i.e. in how many ways can you choose 2 teams from a total 8. You can readily apply the formula for choosing 2 out of 8 as \(= (8x7)/2 = 28\)

The explanation would be something like:
Essentially, we need to find all possible pairs of teams from the 8.

So to create a pair, the first team can be chosen from the total of 8 - so 8 options/ways available. Now for each of this, we can choose the the opponent team for the pair from the 7 teams left. So the total will be \(8 x 7 = 56.\)

Now you can see that when we do the above, we will all possible pairs - (team1, team2), (team2, team3)....etc. We will also get the reverse pair (team2, team1), (team3, team2).... The order shouldn't matter since a game is just between 2 teams irrespective of the order.

So for every such pair of team, the reverse order is also included in the total of 56. So the total number of unique pairs we can have (which is the number of games) \(= 56/2 = 28\).

I was so confused by this line "If each game is played by 2 teams, what is the total number of games played?

I got 28 (coz 7!) then when I see this line "If each game is played by 2 teams, what is the total number
of games played?" I took one extra step to divide 28/2 = 14......although 14 is not a choice but I wonder can ayone pls explain what does this line mean?

The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\).

Answer: C.
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