probability of getting a certain combination when 5 drinks are selected?
At an open bar there are 26 bottles: 6 vodkas, 5 Bacardi, 4 cognac, 4 Seagram’s, and 7 wines. If a guest randomly selects 5 bottles for his table, w...
At an open bar there are 26 bottles: 6 vodkas, 5 Bacardi, 4 cognac, 4 Seagram’s, and 7 wines. If a guest randomly selects 5 bottles for his table, what is the probability that he will get 2 vodkas, 2 Seagram’s, and 1 cognac?
Kinda lost. would appreciate any help, thanks…
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all combinations of 5 bottles from 26 = 26C5 = 65780
—————–
all combinations of 2 vodkas from 6 = 6C2 = 15
all combinations of 2 Seagram’s from 4 = 4C2 = 6
all combinations of 1 Cognac from 4 = 4C1= 4
probability
= (6C2 x 4C2 x 4C1) / 26C5
= 15 x 6 x 4 / 65780 = 0.00547
about 0.55 %
#Thanks for your correction
Another method
6/26 x 5/25 x 4/24 x 3/23 x 4/22 x ( 5! / (2! x 2!))
(1440 / 7893600) x 30 = 432 /78936 = 0.00547 = 0.55%