In an LED light manufacturing facility, an assembly line produces batches of 20 LED lights at a time. Occasionally, due to variations in manufacturing processes, some LED lights might not meet the required luminosity standards. In one particular batch, 5 out of the 20 LED lights are found to be below the luminosity standard. An inspector is tasked with selecting 4 LED lights from each batch to test their luminosity.
(a) How many different test groups can the inspector select that will contain exactly 2 LED lights that are below the standard luminosity?
(b) How many different test groups can the inspector select that will include at least 1 LED light that is below the standard luminosity?

Question

24-06-2024
Mathematics

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In an LED light manufacturing facility, an assembly line produces batches of 20 LED lights at a time. Occasionally, due to variations in manufacturing processes, some LED lights might not meet the required luminosity standards. In one particular batch, 5 out of the 20 LED lights are found to be below the luminosity standard. An inspector is tasked with selecting 4 LED lights from each batch to test their luminosity.
(a) How many different test groups can the inspector select that will contain exactly 2 LED lights that are below the standard luminosity?
(b) How many different test groups can the inspector select that will include at least 1 LED light that is below the standard luminosity?

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