# Permutations and combinations

In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components,in a manner that minimizes the impact of shocks.

One end of the casing is designated as the top and the other end the bottom.

a) how many different designs are possible

b) If the seven components are all identical how many designs are possible

c) If the seven components consist of 3 of one type and 4 of another type how many different designs are possible

Please show detail of solutions i.e. formulas and reasoning

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#### Solution Summary

This uses permutations and combinations in a design problem.

$2.19