Probability/counting question? Help, please? D:?

Question

Help me with a probability question, please?
And if possible.. explain how it works?
Thank you..

Seven boys and three girls are on a soccer team. The A team is to have 5 members. How man possible A teams can I pick? Say the A team must have at least two girls. How many A teams can I pick now?

Answer 1

nCr = n! / [r! * (n - r)!]

So, your first question... "How many possible A teams can I pick"?

You have 10 kids total.
10C5 = 10! / (5!*5!) = 252

Second question:
"The A team must have at least 2 girls."

Here you'd have two possibilities:
2 girls, 3 boys
3 girls, 2 boys
(those are the only possibilities since you only have 3 girls in the group.)

2 girls, 3 boys:
(3C2)*(7C3)
= (3) * (35)
= 105

3 girls, 2 boys:
(3C3) * (7C2)
= (1)*(21)
= 21

So, total ways to choose at least 2 girls for a 5 person team is
(105) + (21) = 126

Answer 2

Recall that (1) For a positive integer k, k! (read "k factorial) means (1)(2)...(k) and 0! = 1. And (2) the number of ways to choose k from n is n!/k!(n-k)!

Thus, the first part of your question is simply the number of ways to choose 5 from the 10 team members, or 10!/5!5! =
252.

The second part has this answer: you may choose either 2 girls and 3 boys or 3 girls and two boys. Thus, choose 2 from 3 and 3 from 7 AND 3 from 3 and 2 from 7 =
(3!/2!1!)(7!/3!4!) + (3!/3!0!)(7!/2!5!) =126.

Answer 3

1) There are 10 people in all. You have to choose 5 out of 10 for the A team.
C(10,5)=10!/(5!5!)=10x9x8x7x6 / 5x4x3x2x1=30240/120=252 ways
2) probability of selecting a girl is 3/10
probabilty of selecting a boy=7/10
This is a Binomial distribution with p=0.3 q=0.7
p=prob of success (selecting a girl)
n=10 p=0.3 x=no of girls
P(x>=2)=p(x=2)+p(x=3)=0.2335+0.2668=0.5003
There are several Binomial probability tables. I used the link below. You'll need to download the Adobe Reader to use this table. You may use a different table.

Answer 4

Initially gender does not matter.
So it's picking 5 out of 10. Simple formula
10C5 = 10! / (5!)^2

With the restriction, you must now consider separate cases.
A. exactly 2 girls (and 3 boys)
So we must pick 2 out of 3 girls, and 3 out of 7 boys.
Answer = 3C2 * 7C3

B. exactly 3 girls
We must pick 3 out of 3 girls, and 2 out of 7 boys
Answer = 3C3 * 7C2 = 1* 7C2

Answer 5

3C2 same as C(3,2)

two girls & 3 boys => 3C2 * 7C3= 105
3 girls & 2 boys => 3C3 * 7C2 = 21

Add 2 ans => 105 + 21 = 126 A teams