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Homework Statement
From 27 pieces of luggage, an airline handler damages a random sample of 4.
The probability that exactly one of the damaged items is insured is twice the probability that none of the damaged pieces are insured.
Calculate the probability that exactly two of the four damaged pieces are insured.
Homework Equations

The Attempt at a Solution
From the second line,
"P(one of the damaged items is insured) = 2 x P(none of the damaged pieces are insured)"
Assuming that the probability of one of the 27 luggage being insured is r/27, I'm trying to work out the two probabilities in the second line... so that I can solve for r, and then use that to answer the actual question "Calculate the probability that exactly two of the four damaged pieces are insured"
I am confused about working out the two probabilities in the second line.
For P(one of the damaged items is insured)... is the answer that there are four possibilities where one of the four damaged items is insured,so:
4 (r/27)(27r1/26)(27r2/25)(27r3/24) ?