SOLUTION: Find the theoretical probability of the event. A technician is launching fireworks near the end of a show. Of the remaining nine fireworks, seven are blue and two are red. If

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Question 1157262: Find the theoretical probability of the event.
A technician is launching fireworks near the end of a show. Of the remaining nine fireworks, seven are blue and two are red. If she launches seven of them in random order, what is the probability that all of them are blue?
Thanks so much for your help!
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) About Me  (Show Source):
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it is 7C7/9C7=1/36 since 9C7 is 9*8*7!/7!*2!=1/36 or 0.028
(7/9)*(6/8)*(5/7)(4/6)(3/5)(2/4)(1/3)=5040/101440 or 0.028

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the probability that any one picked out of the 9 is blue is 7/9.
the probability that any one picked out of the 9 is red is 2/9.
the probability that the first one picked at random is blue is 7/9
the probability that the second one picked at random is blue is 6/8.
this is because the problem is without replacement.
the probability that all 7 are blue is therefore:
7/9 * 6/8 * 5/7 * 4/6 * 3/5 * 2/4 * 1/3 = (7*6*5*4*3*2*1) / (9*8*7*6*5*4*3) = 5040 / 181440 * c(7,7) = .027777777.....