SOLUTION: A box contain 74 brass watchers 86 steel watchers and 40 aluminum watchers three watchers drawn at random from the box without replacement determine the probability that no aluminu

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Question 1153795: A box contain 74 brass watchers 86 steel watchers and 40 aluminum watchers three watchers drawn at random from the box without replacement determine the probability that no aluminum watchers are drawn at random from the box without replacement



Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

There are 74+86+40 = 200 watchers in the box, in all.


Of them,  74+86 = 160 are not aluminum.


Hence, the probability under the problem's question is  P = %28160%2F200%29%2A%28159%2F199%29%2A%28158%2F198%29 = 0.51.     ANSWER

Solved.


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            Tutor @greenestamps used WRONG conception and/or wrong numbers for his calculations.

            If to use  COMBINATIONS,  then the correct way to construct the solution is as follows: 


The number of all possible triples of 200 items is  C%5B200%5D%5E3.


The number of all favorable triples is  C%5B160%5D%5E3.


The probability under the question is the ratio


    P = favorable_triples%2Fall_triples = C%5B160%5D%5E3%2FC%5B200%5D%5E3,


and it leads exactly to the same answer, which I got in my solution above.




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


washers, not watchers....!

Number of ways of choosing 3 of the total 160 washers: C(160,3) = 669920

Number of ways of choosing 3 that are not aluminum -- i.e., choosing 3 of the 120 washers that are not aluminum: C(120,3) = 280840

Probability of choosing 3 of which none are aluminum:

280840/669920 = .4192142345

...OR...

P(1st is not aluminum) = 120/160 = 3/4
P(2nd is not aluminum) = 119/159
P(3rd is not aluminum) = 118/158 = 59/79

P(all 3 are not aluminum) = (3/4)(119/59)(59/79) = 21063/50244 = .4192142345