Question

In a football championship, 153 matches were played. every two teams played one match with each other. the number of teams, participating in the championship was

Answer 1

Let there were x teams participating in the games, then total number of matches,
nC2 = 153.
On solving we get,
=> n =−17 and n =18.
It cannot be negative so,
n = 18 is the answer.

Answer 2

Answer:

No. of teams participated are 18

Step-by-step explanation:

Given : In a football championship, 153 matches were played.

Every two teams played one match with each other.

To Find : Find the number of teams, participating in the championship

Solution:

Let n be the no. of teams

Every two teams played one match with each other.

So, The no. of matches played will be calculated using combination

Formula : $^nC_r=\frac{n!}{r!(n-r)!}$

r = 2

$^nC_2=\frac{n!}{2!(n-2)!}$

We are given that 153 matches were played

So, $\frac{n!}{2!(n-2)!}=153$

$\frac{n(n-1)(n-2)!}{2!(n-2)!}=153$

$\frac{n(n-1)}{2 \times 1}=153$

$n^2-n=306$

$n^2-n-306=0$

$n^2+17n-18n-306=0$

$n(n+17)-18(n+17)=0$

$(n+17)(n-18)=0$

$n=-17 , 18$

Since no. of teams cannot be negative

So, No. of teams participated are 18