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You can select the frst house in 40 ways. You can then select the second in 39 ways, making 39*40 in all. But in doing so you will have selected each pair twice (AB and BA). So the total number is 39*40/2 = 780.

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Q: If 40 houses in a community all had to have direct lines to one another in order to have telephone service how many lines would be necessary?
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