#Number Theory

(a) A population of 120 individuals contains 45 engineers, 30 teachers, and the rest are administrators. A simple random sample of 6 is selected. (i) Probability that exactly 3 engineers are included? (ii) Probability that the sample contains no teachers? (b) A length is measured five times: 12.478 m, 12.463 m, 12.481 m, 12.469 m, 12.472 m. Determine the absolute error between the exact average and the rounded average. (c) Evaluate the argument "Artificial Intelligence will reduce employment because automation replaces human labor." (d) A number leaves remainder 5 when divided by 12 and remainder 4 when divided by 7. Find the smallest such positive integer and its remainder when divided by 9.

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