Statistics? Anyone?
I'd appreciate the help please:)
The grade appeal process at a university requires that a jury be structured by selecting seven individuals randomly from a pool of seven students and seven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of four students and three faculty?

Question

Statistics? Anyone?
I'd appreciate the help please:)
The grade appeal process at a university requires that a jury be structured by selecting seven individuals randomly from a pool of seven students and seven faculty.​ (a) What is the probability of selecting a jury of all​ students? (b) What is the probability of selecting a jury of all​ faculty? (c) What is the probability of selecting a jury of four students and three ​faculty?

zarkon · Answer

do you know the hypergeometric distribution

yanasidlinskiy · Answer

Like the formula?

zarkon · Answer

it is a probability mass function

zarkon · Answer

https://en.wikipedia.org/wiki/Hypergeometric_distribution

yanasidlinskiy · Answer

Ok, then yes I have.

zarkon · Answer

you can use that to answer the question

yanasidlinskiy · Answer

The problem is, is that I don't know how to use that and everything is just confusing me. It's my first attempt so I don't know.

zarkon · Answer

do you know this notation $${n\choose r}$$

yanasidlinskiy · Answer

yea.

zarkon · Answer

ok

P(a students and 7-a faculty chosen)

$$=\Large\frac{{7\choose a}{7\choose 7-a}}{{14\choose 7}}$$

yanasidlinskiy · Answer

Okay, so what's my next step?

zarkon · Answer

replace a with the numbers you need

yanasidlinskiy · Answer

Where do I get the numbers from.... I only have 7 and 14. Unless I'm supposed to add them 2.

zarkon · Answer

"What is the probability of selecting a jury of all​ students? "

all students means a=7  and 


$$=\Large\frac{{7\choose 7}{7\choose 7-7}}{{14\choose 7}}$$

zarkon · Answer

$$=\Large\frac{{7\choose 7}{7\choose 0}}{{14\choose 7}}$$

yanasidlinskiy · Answer

What would I do then?

zarkon · Answer

I've given you one of the answers (after you calculate it from my formula)

I'm not giving all the answers

yanasidlinskiy · Answer

No, I know. I'm just asking because that formula really confuses me.  I've been given this:$$_{n}C _{r} = \frac{ n! }{ r!(n-r)! }$$

zarkon · Answer

$${n\choose r}=  ~_{n}C_r$$

zarkon · Answer

same thing

yanasidlinskiy · Answer

Ohh, wow. Makes sense now. Thanks.

zarkon · Answer

$$=\Large\frac{{7\choose 7}{7\choose 0}}{{14\choose 7}}$$

$$=\Large\frac{_7C_7\cdot _7C_0}{{_{14}C_7}}$$

yanasidlinskiy · Answer

Got it! That's what I needed thanks.