Used photocopy machines are returned to the supplier, cleaned, and then sent bac

Question

Used photocopy machines are returned to the supplier, cleaned, and then sent back out on lease agreements. Major repairs are not made, however and as a result, some customers receive malfunctioning machines. Among eight used photocopiers available today, three are malfunctioning. A customer wants to lease four machines immediately. To meet the customer's deadline, four of the eight machines are randomly selected and, without further checking, shipped to the customer. What is the probability that the customer receives no malfunctioning machines? Your Answer:

Explanation / Answer

Among 8 used photocopiers, 3 are malfunctioning and 5 are not malfunctioning.

Number of ways to choose 4 machines out of 8 machines = C(8,4) = 8! / 4! * (8-4)! = (8*7*6*5) / (4*3*2*1) = 70

Number of ways to choose 4 machines out of 5 non-malfunctioning machines = C(5,4)

= 5! / 4! * (5-4)! = 5

Probability that customer receives no malfunctioning machines =

(Number of ways to choose 4 machines out of 5 non-malfunctioning machines)/(Number of ways to choose 4 machines out of 8 machines)

= 5 / 70 = 1/14 = 0.0714

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