Answer:
105/252 = 0.41666...
Step-by-step explanation:
There are (7C4)(3C1) = (35)(3) = 105 ways to choose exactly 4 boys. There are 10C5 = 252 ways to choose 5 youths, so the probability that a randomly chosen team will consist of exactly 4 boys is ...
105/252
_____
nCk = n!/(k!(n-k!))
Answer:
There is a 41.67% probability that exactly 4 boys are picked in this team of 5.
Step-by-step explanation:
The order is not important, so we use the combinations formula.
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Number of desired outcomes.
Four boys and one girl: So
[tex]C_{7,4}*C_{3,1} = \frac{7!}{4!(7-4)!}*\frac{3!}{1!(3-1)!} = 35*3 = 105[/tex]
Number of total outcomes:
Combination of five from a set of 10.
So
[tex]C_{10,5} = \frac{10!}{5!(10-5)!} = 252[/tex]
What is the probability that exactly 4 boys are picked in this team of 5?
[tex]P = \frac{105}{252} = 0.4167[/tex]
There is a 41.67% probability that exactly 4 boys are picked in this team of 5.
