Question 1203178
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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<br>
Total number of teachers: 10+12+6+8+4 = 40<br>
Number of ways of choosing 2 teachers: "40 choose 2" = C(40,2) = (40*39)/(2*1) = 780<br>
Number of ways of choosing 2 biology teachers: 12 choose 2 = C(12,2) = (12*11)/(2*1) = 66<br>
Number of ways of choosing 2 physics teachers: 4 choose 2 = C(4,2) = (4*3)/(2*1) = 6<br>
ANSWER: probability that either 2 biology or 2 physics teachers are selected = (66+6)/780 = 72/780 = 6/65<br>
With the other interpretation, the number of ways of selecting two teachers who are EITHER biology or physics teachers is<br>
C(16,2)/C(40,2) = 120/780 = 2/13<br>