Question

if the numbervof teams are 15 then, what would be the number of total matches?​

Answer 1

Given,

The total number of teams is = 15

To find,

The total number of matches among the given number of teams.

Solution,

We will solve this mathematical problem by assuming that a team will play a single match against another teams and it is a round robin tournament. ( If that's not the case and there is repeated matches between two teams, then we can multiply the number of repeat matches with the final result.)

Now, we can solve this mathematical problem by using the combination method.

Here,

n = total number of teams = 15

r = total teams per match = 2

Combination = nCr = 15C2 = 105

Hence, atleast 105 will be played.

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

PROCESS : 1

USING ARITHMETIC PROGRESSION

Here total number of teams = 15

In order to organize a match 2 teams are required

So the first team will play 14 matches ( As a team can not play a match with itself )

The second team will play 13 matches ( As second team has played a match before with first team. So it will be not counted when total number of match is concerned )

Similarly for the other teams

Hence the total number of matches

$= 14 + 13 + 12 + 11 + ....... + 3 + 2 + 1$

It is a Arithmetic Progression with

First term = 14

Last term = 1

Number of terms = 15

Hence the total number of matches

$= \displaystyle \: \sf{ \: \frac{14}{2}(14 + 1) \: }$

$= \displaystyle \: \sf{ \: 7 \times 15\: }$

$= 105$

PROCESS : 2

USING COMBINATION

Here total number of teams = 15

Here total number of teams = 15In order to organize a match 2 teams are required

Hence the total number of matches

$= \large{ {}^{15} C_2}$

$\displaystyle \: = \frac{15 \times 14}{2}$

$= 105$

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