In a small chess tournament, 20 matches were played. find out how many people were involved if it is known that each participant played 2 games with every other participant in the tournament.

Step-by-step explanation:

Given :  

20 matches were played in a small chess tournament.

Each participant played 2 games with every other participant in the tournament.

To Find : how many people were involved?

Solution :

Let no. of players involved be n

Since we know that for every match there should be two players out of n

So, number of ways they can play :

We  are also given that  each participant played 2 games with every other participant.

So, total no. of games played  =

Since we are given that total no. games played = 20

⇒

⇒

⇒  --(a)

Formula of combination:

⇒

So, solving (a) further using formula

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒ n = 5 , n =-4

Neglect the negative value since no. of players cannot be negative.

Thus no. of player involved is 5.