Question 1154062
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            To facilitate calculations,  I will use the  Excel' standard function  COMBIN(n,k)  to calculate the number of combinations  {{{C[n]^k}}}.


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Seven different fireworks can be selected from 13 fireworks by  {{{C[13]^7}}} = 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[7]^3*C[6]^4}}} = COMBIN(7,3)*COMBIN(6,4) ways = 35*15 = 525 ways.


The probability under the problems's question is  


    P = {{{favorable/total}}} = {{{525/1716}}} = 0.3059 = 30.59% (approximately).
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Solved.