Of the 30 students in the sixth period math class, 8 are also in the same fourth period science class. Which can be used to determine the probability that if three students are chosen at random from the math class to do a group project, the first student chosen to be in the group is in the fourth period science class but the other two are not?
Answer
A
open paren 8 over 30 close paren times open paren 8 over 30 close paren times open paren 8 over 30 close paren
B
open paren 8 over 30 close paren times open paren 22 over 30 close paren times open paren 21 over 30 close paren
C
open paren 8 over 30 close paren times open paren 22 over 29 close paren times open paren 21 over 28 close paren
D
open paren 8 over 30 close paren times open paren 7 over 29 close paren times open paren 6 over 28 close paren
Explanation
The first student must be one of the 8 students in the science class, so the probability is 8/30. After that student is chosen, 29 students remain, and all 22 who are not in the science class are still available, giving 22/29 for the second choice. Then 28 students remain, with 21 not in the science class, giving 21/28 for the third choice. Thus the probability is represented by choice C.
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