Question

In a cricket cup total of 153 matches were played and every two teams played exactly one match with each other. So, what was the total number of teams participating in the Cricket Cup?

Options

• 15

• 16

• 17

• 18

Answer 1

18
Explanation:
Let's suppose there were x number of team in the cricket cup then from the given statement we have

`"^nC_2=153⇒(n!)/(2!(n-2)!)=153`

⇒ `(n(n-1)(n-2)!)/(2(n-2)!)=153`

⇒ `n^2-n-306=0`

⇒(n - 18)(n +17) = 0

n =18 and n = -17
As answer cannot be negative
So, n = 18