1. ## probability

at the whistle top cafe,15 of the 19 patrons are mechanics. If a sample of 8 is taken, what is the probability that exactly 5 patrons are mechanics

2. Hello, Dan!

At the Whistle Top Cafe,15 of the 19 patrons are mechanics.
If a sample of 8 is taken, what is the probability that exactly 5 patrons are mechanics?

There are 19 patrons: 15 Mechanics and 4 Others.

There are: .$\displaystyle _{19}C_8 \:=\:75,\!592$ possible samples.

We want 5 Mechanics and 3 Others.
. . There are: .$\displaystyle \left(_{15}C_5\right)\left(_4C_3\right) \;=\;25,\!740$ ways.

Therefore: .$\displaystyle P(\text{5 Mechanics, 3 Others}) ;=\;\frac{25,\!740}{75,\!582} \;=\;\frac{110}{323}$

But check my arithmetic, please . . .
.

3. Originally Posted by dan123
at the whistle top cafe,15 of the 19 patrons are mechanics. If a sample of 8 is taken, what is the probability that exactly 5 patrons are mechanics
dan123;328355,
You need to learn some very basic properties of combinations.
You also need to show some effort on your own part.

p.s.
Of course there is always someone who does other people’s work for them.
But be warned, Soraban will not be with you at test time.