Question

in a cricket championship,there are 21 matches.if each team plays one match with every other team.then the number of teams are?​

Answer 1

Answer:

7

Step-by-step explanation:

Let number of teams be n

nC2= 21

n(n-1)/2 = 21

n(n-1)= 42

42 can be written as 7*6

n(n-1)=7(6)

Therefore n=7

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Answer 2

Given: In a cricket championship there are 21 matches. Each team plays one match with every other team.

To find: Number of teams in the championship

Explanation: Let the number of teams be n. Since a match consists of two teams, any two teams can be selected at random from n teams.

To select any two teams, the number of ways are

$\binom{n}{2}$

Now, these number of ways are equal to number of matches played .

Therefore,

$\binom{n}{2} = 21$

=> n! / (n-2)! 2! = 21

=> n(n-1) = 21*2 [since n! = n (n-1) (n-2)!]

=> n(n-1) = 42

=> ${n}^{2} - n - 42 = 0$

=> (n-7)(n+6) = 0

=> n= 7,-6

Since number of teams cannot be negative, therefore n=7

Therefore, number of teams in the championship is 7.