Eight devices for example printers d1 d2 d3 d4 d5 d6 d7 d8 c

Eight devices (for example printers) d1, d2, d3, d4, d5, d6, d7, d8 connect with a central processor, which polls them in order so that it can identify one that is ready to communicate. Suppose that four are ready to communicate when the polling cycle starts. The probability that the central processor issue exactly two polling requests, which fail before issuing the next request, which succeeds = ________________

Please help - My notes aren\'t helping so a step solution is strongly requested

Solution

Total number of device = 8

Number of device ready to communicate = 4

Number of device not ready to communicate = 4

Therefore, probability that the central processor issue exactly 2 polling requests which fail, before issuing the next request which succeeds = Probabilty that first 2 polling request goes to the devices that are not ready to communicate x Probabilty that the third polling request goes to the devices that is ready to communicate                    = 4/8 x 3/7 x 4/6 = 1/7