SOLUTION: A technician is launching fireworks near the end of a show. Of the remaining thirteen fireworks, seven are blue and six are red. If he launches seven of them in a random order, wha
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Question 1154062: A technician is launching fireworks near the end of a show. Of the remaining thirteen fireworks, seven are blue and six are red. If he launches seven of them in a random order, what is the probability that exactly 3 of them are blue ones? Answer by ikleyn(52794) (Show Source):
To facilitate calculations, I will use the Excel' standard function COMBIN(n,k) to calculate the number of combinations .
Seven different fireworks can be selected from 13 fireworks by = COMBIN(13,7) = 1716 ways.
It is the sample space number of elements.
The favorable 7-element subsets are those that consist of 3 blue and 7-3 = 4 red fireworks.
You can form such subsets by = COMBIN(7,3)*COMBIN(6,4) ways = 35*15 = 525 ways.
The probability under the problems's question is
P = = = 0.3059 = 30.59% (approximately).
