Combination Puzzle for Nikolaus 2006

This year we got the following request from a non-mathematician: Given the numbers 1, 3, 4 and 6. Order them, put three from the operators +, -, * or / between them and add some parentheses such that the result of the expression is 24. The person knew the solution

6 / (1 - 3 / 4) = 24

and wanted to know if there are more solutions (no, this is the only one).

In this Nikolaus puzzle you get three similar questions: For each question you are given four numbers and a result number. How many possibilities are there to order the four numbers and to put three operators from +, -, * or / between them such that for some choice of parentheses we get an expression that evaluates to the result number?

Note that we just count the different orderings of the numbers and different operators (and not the number of possibilities for the setting of parantheses - to avoid a complicated definition for such a counting).

[Get a New Puzzle]

Questions and suggestions to Frank.Luebeck@Math.RWTH-Aachen.De.