SOLUTION: At the end of each week, a generous teacher gives some candy to a few randomly selected students. There are 30 students in this teacher's class - 16 girls and 14 boys. A) If the t

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Question 1174377: At the end of each week, a generous teacher gives some candy to a few randomly selected students. There are 30 students in this teacher's class - 16 girls and 14 boys.
A) If the teacher wanted to give candy to 6 of the students, how many possible groups of 6 students can she choose?
B) To avoid appearing to favor one gender, the teacher will randomly choose 3 of the 16 girls and 3 of the 14 boys. How many possible groups of 6 can she choose?
C) Find the probability that the teacher gives candy to 3 boys and 3 girls if she chooses 6 students from the class at random.

Answer by ikleyn(52786) About Me  (Show Source):
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(A)  It is the number of combinations of 30 students taken 6 at a time


         N =   C%5B30%5D%5E6 = %2830%2A29%2A28%2A27%2A26%2A25%29%2F%281%2A2%2A3%2A4%2A5%2A6%29 = 593775.    ANSWER



(B)  n = C%5B16%5D%5E3.C%5B14%5D%5E3 = %2816%2A15%2A14%29%2F%281%2A2%2A3%29.%2814%2A13%2A12%29%2F%281%2A2%2A3%29 = 560*364 = 203840.    ANSWER



(C)  This probability is the ratio of the numbers n and N, found in (A) and (B), respectively


          P = n%2FN = 203840%2F593775 = 448%2F1305 = 0.343295.     ANSWER

Solved.