This is more of a combinatorics problem. Consider an engineering firm that produ

Question

This is more of a combinatorics problem.

Consider an engineering firm that produces 8 distinct products. The company surveys its customers concerning the products. Based on survey results, the company will categorize each of the products as either

"keep producing", "borderline", or "drop".

a) How many different ways can the categories be assigned to the 8 products?

This is 8^3=512.

Please help with B.

b) Now assume that company management has decided that at least one product must be put

in each of the 3 categories. How many different assignments are possible with this restriction?

Explanation / Answer

A) given answer is correct, i.e 83 = 512

B) the number of assignments are possible with this restriction = 33 = 27

So answer is 27

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