The editor of an anthology of short stories has to select authors from a pool of 12 authors, of which 4 are female. If the anthology is to include the work of 8 authors of which at least 2 must be female, in how many ways can the editor select the authors?
Choose the most appropriate option:
A) 168
B) 201
C) 294
D) 462
E) 495
we have total 12 authors. we need to select 8. we have 8 males and 4 females.   we need to select in a such way, that at least 2 females are selected.   my first step:   12C8 = 495.   since this is a total number of combinations that we can have, regardless of the restrictions, we can eliminate right away A, B, C, and E.   why A, B, C - because the number of combinations when the restrictions are not respected is way smaller than the number of combinations in which the restrictions are respected.   nevertheless, I wanted to check further, so that to make sure I get the right answer:   second step, to get "at least 2 females", we need to deduct from 495 number of combinations when we have 8 males 0 females and when we have 7 males and 1 female.   8 males 7 females:   8C8 * 4C0 = 8   7 males and 1 female: 8C7*4C1=32.   Thus, the required number of combinations = Total - case with 0 females - case with 1 female = 495-1-32= 
<gadget id="calculator">495-1-32</gadget>
<output>462</output>
462.   462 is the correct answer.
<result>D</result>
The editor of an anthology of short stories has to select authors from a pool of 12 authors, of which 4 are female. If the anthology is to include the work of 8 authors of which at least 2 must be female, in how many ways can the editor select the authors?