A group of 24 workers, comprising 8 men, 8 women and 8 boys is assigned a piece of work. No two workers in the group have the same capacity to work. Each day, a sub-group of workers, comprising 1 man, 1 woman and 1 boy, work together. In this manner, sub-groups of all possible combinations comprising one man, one woman and one child work on exactly one day each, and the work is completed on the last day, taking a total of 512 days. If all the 24 workers work together for one day, what part of the entire work will be completed
Question
A group of 24 workers, comprising 8 men, 8 women and 8 boys is assigned a piece of work. No two workers in the group have the same capacity to work. Each day, a sub-group of workers, comprising 1 man, 1 woman and 1 boy, work together. In this manner, sub-groups of all possible combinations comprising one man, one woman and one child work on exactly one day each, and the work is completed on the last day, taking a total of 512 days. If all the 24 workers work together for one day, what part of the entire work will be completed
Solution
The problem states that there are 24 workers divided into 8 men, 8 women, and 8 boys. Each day, a subgroup of 1 man, 1 woman, and 1 boy work together. This means that there are 888 = 512 different combinations of workers, which is why the work takes 512 days to complete.
If all 24 workers work together for one day, they would complete 1/512 of the work. This is because the total work is defined by the 512 unique combinations of workers, and each combination completes a portion of the work in one day. Therefore, if all the workers work together, they would complete the same amount of work that one unique combination of workers would complete in one day.
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