Concept
How can the counting rule handle positions with different numbers of choices?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Suppose Virginia outlawed personalized plates and gave everyone a randomly generated 7-character plate. Furthermore, the last four characters of the plate had to be digits instead of letters, so that something like “RFP-6YQ7” would be impossible. In this case, not each of the k parts has an equal number of choices. n₁ through n₃ are still 36, but now n₄ through n₇ are just 10. So this gives us: 36 × 36 × 36 × 10 × 10 × 10 × 10 = 466,560,000 plates, or only about .006 times as many as before. Better stick with alphanumeric characters for all seven positions."
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