Problems based on Numbers Test 4

Question : 25 of 40

Marks: +1, -0

In a football championship, 153 matches were played. Every two teams played one match with each other. The total number of teams, participated in the championship were:

Validate

Solution:

Total number of matches played =

^n C_2

where, n = number of terms.
Match is played between two teams

^ n C_2 = 153

matches

{n!}/{2!(n-2)!}=153

{n(n-1)(n-2)!}/{2(n-2)!}=153

n^2-n=306

n^2-n-306=0

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

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

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

n + 17 = 0

, Rejected

n - 18 = 0

n = 8

So, the number of teams 18

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