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2. (+10 point) In the design of an electromechanical product, 6 components are to be stacked into a cylindrical casing in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom and the other end is the top. (a) If all components are different, how many different designs are possible? (b) If 3 components are identical to one another, but the others are different, how many different designs are possible?
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Answer #1

(a) Since all components are different, every arrangement of the components comprises a different design.

Since there are 6 components to be stacked, number of possible different designs = 6!=720.

(b) Since 3 components are identical and others are different, possible number of different designs = \frac{6!}{3!1!1!1!}=\frac{720}{6}=120

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