Question 1205797
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Colby is the producer of the local talent competition show, Homegrown Superstars, 
and needs to form a panel of judges to evaluate performances. 
Colby has a list of 6 musicians and 8 actors from which to select the judging panel.
a. How many ways are there for Colby to select 5 judges, if the order does not matter?
b. If Colby randomly selects 5 judges, what is the probability that he will choose 2 musicians and 3 actors?
c. If Colby randomly selects 5 judges, what is the probability that at least one of them will be a actor?
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<pre>
(a)  {{{C[6+8]^5}}} = {{{C[14]^5}}} = {{{(14*13*12*11*10)/(1*2*3*4*5)}}} = 2002 possible combinations.    <U>ANSWER</U>




(b)  {{{C[6]^2*C[8]^3)/C{14]^5}}} = {{{(15*56)/2002}}} = 0.41958  (rounded).    <U>ANSWER</U>  




(c)  The complementary event is 5 judges with no actors (i.e. all judges are musicians)

     The probability for this complementary event is  P' = {{{C[6]^5/C[14]^5}}} = {{{6/2002}}} = 0.002997  (rounded).   <U>ANSWER</U>

     Therefore, the probability of the event under the question is 

          1 - P' = 1 - 0.002997 = 0.997003  (rounded).
</pre>

Solved.