SOLUTION: A researcher is working with a group of 14 participants, 8 of whom are female and 6 of whom are male. The researcher will select one participant from the group at random, and then

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Question 1140205: A researcher is working with a group of 14 participants, 8 of whom are female and 6 of whom are male. The researcher will select one participant from the group at random, and then she will select a second participant at random from the remaining participants. What is the probability that two females will be selected?
Answer by greenestamps(13203) About Me  (Show Source):
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(1) from the basic definition of probability....

8 females to choose from out of 14 total for the first; 7 females out of 13 total remaining for the second:
(8/14)*(7/13)

Simplify if required....

(2) using "n choose r" concept....

The number of ways of choosing 2 of the 8 females = 8 choose 2;
the total number of ways of choosing 2 of the 14 participants = 14 choose 2

P(choose 2 females) = C(8,2)/C(14,2)