Respuesta :
Answer: The fraction 1/30
=========================================================
Explanation:
4 girls + 6 boys = 10 students total
n = 10 people to pick from
r = 3 selections
Use the nCr combination formula
n C r = (n!)/(r!(n-r)!)
10 C 3 = (10!)/(3!*(10-3)!)
10 C 3 = (10!)/(3!*7!)
10 C 3 = (10*9*8*7!)/(3!*7!)
10 C 3 = (10*9*8)/(3!)
10 C 3 = (10*9*8)/(3*2*1)
10 C 3 = (720)/(6)
10 C 3 = 120
This tells us there are 120 different debate teams possible. Order doesn't matter.
------------------
Of those 120 teams, only 4 of them have all three girls.
Consider the girls with code names A,B,C,D
One team is {A,B,C}
Another is {B,C,D}
Another is {A,B,D}
The last is {A,C,D}
Or you could note that there are 4 ways to not select a particular girl, which leads to the four teams of all girls.
Yet another path you can take is to compute nCr for n = 4 and r = 3. You should get 4 C 3 = 4.
-----------------
We found there are 4 ways to have a team of all girls and no boys, out of 120 ways to form a team.
4/120 = (1*4)/(30*4) = 1/30 is the final answer
This is approximately equal to 1/30 = 0.0333 = 3.33%
