Respuesta :
1. In how many games does a girl play against a boy?
A: Because there are 5 girls, each will play against 5 boys, so in total is 5*5 = 25 times.
2. In how many games does a girl play against another girl?
A: In this case, we only need to calculate how many girl pairs are there among these 5 girls, and it become a combination problem which can solved by [tex]C^{2}_{5}=\frac{5*4}{2*1}=10[/tex]
3.The fraction of games "B vs B" should be the number of "B vs B" (which is 10) divide the total number of the games "B vs B" & "G vs G" & "B vs G" (which is 10+10+25=45, see the analysis in 1.A and 2.A), so the fraction should be 10/45=2/9
4.One person will have to play against 9 people at the tournament, and the total number of the games is 45, so the fraction should be 9/45 = 1/5
A: Because there are 5 girls, each will play against 5 boys, so in total is 5*5 = 25 times.
2. In how many games does a girl play against another girl?
A: In this case, we only need to calculate how many girl pairs are there among these 5 girls, and it become a combination problem which can solved by [tex]C^{2}_{5}=\frac{5*4}{2*1}=10[/tex]
3.The fraction of games "B vs B" should be the number of "B vs B" (which is 10) divide the total number of the games "B vs B" & "G vs G" & "B vs G" (which is 10+10+25=45, see the analysis in 1.A and 2.A), so the fraction should be 10/45=2/9
4.One person will have to play against 9 people at the tournament, and the total number of the games is 45, so the fraction should be 9/45 = 1/5
The total number of games a girl play against a boy is 25, the number of games a girl plays against a boy is 10, the fraction of the games are boy-versus-boy is 2/9, and 1/5 fraction of all games at the tournament Anita plays the game.
What are permutation and combination?
A permutation can be defined as the number of ways a set can be arranged, order matters but in combination, the order does not matter.
We have 5 girls and 5 boys in a chess club:
There are a total of 5×5 games girls play against a boy.
= 5×5
= 25
The number of games a girl play against another.
It is a combination problem so the total number of games:
[tex]= _{5}^{}\textrm{C}_r[/tex]
= 10
A fraction of the games are boy-versus-boy:
The number games boy-versus-boy = 10
The number games "Boy vs Boy" & "Girl vs Girl" & "Boy vs Girl"
= 10+10+25
= 45
So the fraction = 10/45 ⇒ 2/9
If Anita is one of the club members then Anita will have to play against 9 people at the tournament.
Total number of games = 45
Then the fraction = 9/45 ⇒ 1/5
Thus, the total number of games a girl play against a boy is 25, the number of games a girl plays against a boy is 10, the fraction of the games are boy-versus-boy is 2/9, and 1/5 fraction of all games at the tournament Anita play the game.
Learn more about combination here:
https://brainly.com/question/4546043
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