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
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 . . .
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