Question 1203178: In a certain school, the principal gave the analysis of the qualified subject teachers in the school as follows:
English teachers = 10
Biology teachers = 12
French teachers = 6
Mathematics teachers = 8
Physics teachers = 4
If two teachers are to represent the school in a workshop, what is the probability that both will come from either Biology or Physics?
Answer by greenestamps(13214)   (Show Source):
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NOTE: There are two interpretations of the problem.
(1) both are biology teachers or both are physics teachers
(2) both are either biology teachers or physics teachers
Total number of teachers: 10+12+6+8+4 = 40
Number of ways of choosing 2 teachers: "40 choose 2" = C(40,2) = (40*39)/(2*1) = 780
Number of ways of choosing 2 biology teachers: 12 choose 2 = C(12,2) = (12*11)/(2*1) = 66
Number of ways of choosing 2 physics teachers: 4 choose 2 = C(4,2) = (4*3)/(2*1) = 6
ANSWER: probability that either 2 biology or 2 physics teachers are selected = (66+6)/780 = 72/780 = 6/65
With the other interpretation, the number of ways of selecting two teachers who are EITHER biology or physics teachers is
C(16,2)/C(40,2) = 120/780 = 2/13
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