Question 1143167
.
<pre>

1.  It is the same as the probability that all 8 are males.


        P = {{{C[21]^8/C[50]^8}}},  or, which is the same,  


        P = {{{(21/50)*(20/49)*(19/48)*(18/47)*(17/46)*(16/45)*(15/44)*(14/43)}}}.


    They are not only "different formulas" - they go with different explanations (=self-explanations),

    but they produce identical results.



2.  P = {{{(C[21]^5*C[29]^3)/C[50]^8}}}.


3.  P (at least 6 of the 8 are females) = P(0 males) + P(1 male) + P(2 males) = {{{C[29]^8/C[50]^8}}} + {{{21*C[28]^7/C[50]^8}}} + {{{C[21]^2*C[27]^6/C[50]^8}}}.


4.  P (at least 2 of the 8 are males)   = complement to P(at most 1 of the 8 is male) = 1 - P(0 males) + P(1 male) = 1 - {{{C[29]^8/C[50]^8}}} - {{{(C[28]^7*21)/C[50]^8}}}.
</pre>