If total teams are 11, what will be the total number of matches in league tournament?
Answers
Answer:
FOR EXAMPLE,,, 10 MATCHES,,,,
By simple permutation and combination,if we start with 1 team ,it has to play 9 matches.the 2nd team will also have to play 9 matches,but we exclude the match played with team ,so effectively while counting it is 8. In this way,all teams must play 9 matches.
By simple permutation and combination,if we start with 1 team ,it has to play 9 matches.the 2nd team will also have to play 9 matches,but we exclude the match played with team ,so effectively while counting it is 8. In this way,all teams must play 9 matches.Thus,total no. Of matches :9+8+7+6+5+4+3+2+1
By simple permutation and combination,if we start with 1 team ,it has to play 9 matches.the 2nd team will also have to play 9 matches,but we exclude the match played with team ,so effectively while counting it is 8. In this way,all teams must play 9 matches.Thus,total no. Of matches :9+8+7+6+5+4+3+2+1That is,45 matches.
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Answer:
The total number of matches are 55.
Given:
total number of teams , N = 11
each team plays against each team only one match.
To Find:
find the total number of matches.
Explanation:
Total number of teams.
Each team has to play against each team only once,
So we have to select two teams each team , so it is the case of combination.
number of ways we can select r members from n members is given by nCr.
similarly , number of ways we can select two teams from 11 teams is given by ¹¹C₂
¹¹C₂ = 11!/(9! . 2!)
= 11 x10/2
=11x5
=55
Hence the total number of matches are 55.