Probability of selecting exactly 3 male is equals to
" Probability is defined as the ration of the number of favourable outcomes to the total number of outcomes."
Formula used
Probability = [tex]\frac{n(S)}{n(T)}[/tex]
[tex]n(S) =[/tex] Number of favourable outcomes
[tex]n(T)=[/tex] Total number of outcomes
According to the question,
Total number of males [tex]=10[/tex]
Total number of females [tex]=10[/tex]
Number of judges for a panel to be selected [tex]=6[/tex]
As per given condition ,
Total number of outcomes [tex]= 20\rm C_{6}[/tex]
Number of selecting exactly 3 males for 6 judges [tex]= 10\rm C_3\times 10\rm C_3[/tex]
Substitute the value in the formula to get the required probability,
Probability of selecting exactly 3 males [tex]= \frac{ 10\rm C_3\times 10\rm C_3}{20\rm C_{6}}[/tex]
[tex]= \frac{120}{323}[/tex]
Hence, the probability of selecting exactly 3 males is equals to [tex]\frac{120}{323}[/tex].
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