SOLUTION: 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 environment. Using combination

Algebra ->  Probability-and-statistics -> SOLUTION: 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 environment. Using combination      Log On


   

Question 467666: 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 environment. Using combinations, find the probability of choosing 6 first shift workers and 2 second shift workers.
Found 2 solutions by ccs2011, stanbon:
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
There are a total of 41 workers 24+%2B+17+=+41
A total of 8 are chosen, thus the total number of combinations is (41 C 8)
41 C 8 = %2841%21%29%2F%288%21%2841-8%29%21%29
6 out of 24 are chosen among the first-shift workers
The number of combinations of choosing 6 out of 24 is (24 C 6)
24 C 6 = %2824%21%29%2F%286%21%2824-6%29%21%29
2 out of 17 are chosen among the 2nd-shift workers
The number of combinations of choosing 2 out of 17 is (17 C 2)
17 C 2 = %2817%21%29%2F%282%21%2817-2%29%21%29
The desired probability is the number of combinations of 6 1st shift workers and 2 2nd shift workers divided by the total number of possible 8-worker combinations
=> P+=+%2824+C+6%29%2817+C+2%29%2F+%2841+C+8%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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 environment. Using combinations, find the probability of choosing 6 first shift workers and 2 second shift workers.
------
Ways to pick 6 first and 2 second shift workers: 24C6*17C2
----
Ways to pick 8 workers randomly: 41C8
------
Answwer: P(6 first and 2 second) = [24C6*17C2]/41C8 = 0.1916
===============
Cheers,
Stan H.