Question

eight teams are to play against each other five times in a tournament. how many matches will be played?​

Answer 1

Answer

140 matches

Step-by-step explanation:

let's say the eight teams are A, B, C, D, E, F,G and H

then, the matches will be like;

A-B , A-C , A-D , A-E , A-F, A-G , A-H , B-C , B-D , B-E , B-F , B-G , B-H , C-D , C-E , C-F , C-G , C - H , D - E , D - F , D - G , D - H , E - F, E - G , E - H , F - G , F - H , G - H

that makes it 28 matches.

Now these matches are played 5 times, so 28 × 5 = 140

∴ 140 matches  are played in the tournament

Answer 2

Answer:

140

Step-by-step explanation:

First, to start simple, let us assess one team, and this will be our 1st team, let's call it Team 1. Team 1 is to play against each team five times, we have eight teams, but Team 1 is only playing against SEVEN other teams (since Team 1 is part of the eight teams), and so for Team 1, it is playing against all other seven teams 5 times.

Team 1: 7×5=35

Now, let's move to Team 2. Team 2 is playing against all other seven teams (again, because its part total eight teams), five times, but, it already played 5 matches with Team 1 already, right? because when we calculated the total of matches played by Team 1, we already counted in the matches it played with Team 2, five matches, so, that means, we cannot repeat it here. So, we remove one team from the total.

Team 2: 6×5=30 6, because it only played 5 matches against the six other teams, and we've already counted in the match it played with Team 1 in the previous calculation, so by making it a 7, we're saying that Team 1 and Team 2 played a total of 10 matches, and that is incorrect.

Now, Let's move on to Team 3. It is must play 5 matches against each team, but, we have already counted its matches BOTH with Team 1 AND Team 2 (since in the calculations of Team 1 and team 2, we calculated the match it played with ALL other teams, and Team 3 is one of them), so, we only calculate the numeber of matches with the rest of the teams it hasn't played with, which are a total of 5 teams. Do you see the pattern here?

Team 3: 5×5=25 Again, we did this since we already calculated the matches Team 3 played with both Team 1 and Team 2, so we do not count it again.

And so, if you've realized the pattern, and realized the situation of the problem, it will make sense to you.

Now, we may deduce an expression for each calculation, when assessing each team,

Team 1: 7×5=35 Team 5: 3×5=15

Team 2: 6×5=30 Team 6: 2×5=10

Team 3: 5×5=25 Team 7: 1×5=5

Team 4: 4×5=20

Now, why did we stop at Team 7? shouldn't we still have a calculation for Team 8? Actually, that would be incorrect, since this is like saying that Team 8 is playing 5 matches with..... no one, a non existent team, but should we still have a calculation for Team 8? Well, actually, we already calculated all of its matches played with all other teams; since we already calculated for each team, the matches it played with all other teams, and Team 8 was included in each calculation, so, calculating any matches now with Team 8, would repeat matches that we've already counted, so that would be incorrect. and yet the calculation would be Team 8: 0×5=0 0 matches

So now, with all the calculations, we reach to an expression: {7×5}+{6×5}+{5×5}+{4×5}+{3×5}+{2×5}+{1×5} = 140

So, the total number of matches played is 140