SOLUTION: Cuold you please help me understand what formula to use for this problem? A warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen

Question 1006522: Cuold you please help me understand what formula to use for this problem?
A warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work enviironment. Find the probability of choosing six first-shift workers.
I tried this formula: 24C6*17C2/41C8. The textbook shows the answer to be .192, but I could find no examples of this type of problem.
Thank you for your help.
Found 3 solutions by MathLover1, Boreal, KMST:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
A warehouse employs workers on first shift and workers on second shift.
Eight workers are chosen at random to be interviewed about the work environment.
Using combinations, find the probability of choosing first shift workers and second shift workers.
Ways to pick first and second shift workers:

Ways to pick workers randomly:

Answwer:

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Your work is correct, and the answer is 0.1915 or 0.192
Check 17C2=I did it by 17*16/2, which is 136.
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
If this does not fully explain what you did not learn or did not understand, feel free to ask me via a thank you note in this website.

There is a total of workers.
There are possible different sets of workers that can be made from those workers.
Some of those sets will have
of the workers on first shift and
of the workers on second shift.
How many such sets are possible?
Since there are
possible different sets of workers that can be made from the workers on first shift and
possible different sets of workers that can be made from the workers on second shift,
there are possible different sets of workers made up of exactly workers from first shift and workers from second shift.
Those sets are of the total possible sets of workers,
and that fraction is the probability of getting exactly workers from first shift and workers from second shift:

CAUTION:
Beware of a common mistake.
If you try entering that calculation into your calculator, you must enter
95548245 / ( 134596 X 136 ) = or
95548245 / 134596 / 136 = ,
because that long horizontal line between and
means that must be calculated first, so in other words
that line implies the parentheses around .
If you do not enter the parentheses, you are doing the indicated operations in order from left to right:
you are first dividing by 134596,
and then multiplying the result times 136, so you get
95548245 / 134596 X 136 =(rounded) ,
which is ridiculous, because probabilities cannot be more than 1.00.
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