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(52797)   (Show Source): You can put this solution on YOUR website!
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            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).

Solved.


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