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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.

            To facilitate calculations,  I will use the  Excel' standard function  COMBIN(n,k)  to calculate the number of combinations  C%5Bn%5D%5Ek. 

Seven different fireworks can be selected from 13 fireworks by  C%5B13%5D%5E7 = 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  C%5B7%5D%5E3%2AC%5B6%5D%5E4 = COMBIN(7,3)*COMBIN(6,4) ways = 35*15 = 525 ways.


The probability under the problems's question is  


    P = favorable%2Ftotal = 525%2F1716 = 0.3059 = 30.59% (approximately).

Solved.