Probability of girls on a team getting shirts with pair numbers

[Purpleshinyrock]

Summary:: probability, Probability and Combinatorics

Hello, I need someone to check If I correctly analized the probability of the following event:

A group of younglings formed by 5 girls and 5 boys, Is going to divide in two teams of 5 elements each to play a game.
a) suposing that the division is made randomly, what is the probability of the two teams having elements of only one gender?
What I did Probabiliry(P)=number of possible events N(e)/number of total events N(s)
N(e)= there's only one way of picking 5 girls since it is a team of 5 elements so N(e)=1
N(s)=ways I can pick 5 people out of 10 (I used combinatorics to find) N(s)=252
p(a)=1/252
b)The group has 10 shirts numbered 1 to 10.Suposing that they are distributed randomly, what is the probability that all of the girls getting a shirt with a pair number
solution:
N(e) =pair numbers{2,4,6,8,10}=5
N(s)=ways of people getting shirts =10!
P(b)=5/(10!)=1/725760

c) during the end of the game the 10 students make a line in order to take a photo.Suposing that they all have different heights what is the probability of them getting ordered by their height
solution:
N(e): order biggest to smallest(1)+ smallest to biggest(1)=2
N(s)=10! ways of getting ordered in a line.
P=2/(10!)

Thank You for your time.

 

[PeroK]

Summary:: probability, Probability and Combinatorics

Hello, I need someone to check If I correctly analized the probability of the following event:

A group of younglings formed by 5 girls and 5 boys, Is going to divide in two teams of 5 elements each to play a game.
a) suposing that the division is made randomly, what is the probability of the two teams having elements of only one gender?
What I did Probabiliry(P)=number of possible events N(e)/number of total events N(s)
N(e)= there's only one way of picking 5 girls since it is a team of 5 elements so N(e)=1
N(s)=ways I can pick 5 people out of 10 (I used combinatorics to find) N(s)=252
p(a)=1/252
b)The group has 10 shirts numbered 1 to 10.Suposing that they are distributed randomly, what is the probability that all of the girls getting a shirt with a pair number
solution:
N(e) =pair numbers{2,4,6,8,10}=5
N(s)=ways of people getting shirts =10!
P(b)=5/(10!)=1/725760

c) during the end of the game the 10 students make a line in order to take a photo.Suposing that they all have different heights what is the probability of them getting ordered by their height
solution:
N(e): order biggest to smallest(1)+ smallest to biggest(1)=2
N(s)=10! ways of getting ordered in a line.
P=2/(10!)

Thank You for your time.

a) Not quite.

b) Why is this significantly different from a)? Suppose the teams are decided by who gets the even numbered shirts?

c) Looks right, asssuming they are positioned at random.

 

[WWGD]

Summary:: probability, Probability and Combinatorics

Hello, I need someone to check If I correctly analized the probability of the following event:

A group of younglings formed by 5 girls and 5 boys, Is going to divide in two teams of 5 elements each to play a game.
a) suposing that the division is made randomly, what is the probability of the two teams having elements of only one gender?
What I did Probabiliry(P)=number of possible events N(e)/number of total events N(s)
N(e)= there's only one way of picking 5 girls since it is a team of 5 elements so N(e)=1
N(s)=ways I can pick 5 people out of 10 (I used combinatorics to find) N(s)=252
p(a)=1/252
b)The group has 10 shirts numbered 1 to 10.Suposing that they are distributed randomly, what is the probability that all of the girls getting a shirt with a pair number
solution:
N(e) =pair numbers{2,4,6,8,10}=5
N(s)=ways of people getting shirts =10!
P(b)=5/(10!)=1/725760

c) during the end of the game the 10 students make a line in order to take a photo.Suposing that they all have different heights what is the probability of them getting ordered by their height
solution:
N(e): order biggest to smallest(1)+ smallest to biggest(1)=2
N(s)=10! ways of getting ordered in a line.
P=2/(10!)

Thank You for your time.

I assume you're a native Spanish speaker because you use "pair number" . I guess you mean an even number, i.e , a multiple of 2?

 

[Purpleshinyrock]

I assume you're a native Spanish speaker because you use "pair number" . I guess you mean an even number, i.e , a multiple of 2?

yes its an even number