Question

An archaeologist numbers some articles 1 to 11 in the order he discovers them. He selects at random a sample of 3 of them. What is the probability that the sum of the numbers on the items he selects is less than or equal to 8? (You do not need to list all combinations of 3 items from 11 to answer this question.)

        If the archaeologist believed that items belonging to the more recent of two civilizations were more likely to be found earlier in his dig and of his 11 items 3 are identified as belonging to that more recent civilization (but the remaining 8 come from an earlier civilization) does a rank sum of 8 for the 3 matching the more recent civilization provide reasonable support for his theory?

Answer 1

total number of combination = 11C3 = 11 *10*9/6 = 165

x1 +x2 +x3 <= 8    ,   1=<= xi <= 11, xi are different

following are possible combination

(1,2,3)

(1,2,4)

(1,2,5)

hence required probability= 3/165=1/55

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