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**HallsofIvy** Exactly what do you mean by "sums". In "United States English" we mean specifically "adding" while "British English" encompasses all kinds of calculations. What operations are you allowed to use?

. There are 6 choices for the first digit, 5 choices for the second digit, 4 for the third, etc.

There are 6 choices for the first person to put into the first group, 5 choices for the second person to put into the first group, 4 choices for the first person to put into the second group etc. The difference between this and problem two is that this problem say "three groups"- it does NOT specify a 'first group', 'second group', 'third group'. So you have to **divide** by the number of ways of "ordering" the three groups- there are three ways to choose a "first group", two ways to choose a "second group"- and then of course, there the last group is fixed.