Question

For many years, the state of California used 3 letters followed by 3 digits on its automobile license plates (a) How many different license plates are possible with this arrangement? (b) When the state ran out of new plates, the order was reversed to 3 digits followed by 3 letters. How many additional plates were then possible? (c) When the plates described in part (b) were also used up, the state then issued plates with 1 letter followed by 3 digits and then 3 letters. How many plates does this scheme provide?

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Remember that the fundamental principle of counting states that for a number of independent events nn where the first event can occur in m1m_1 ways, the second in m2m_2, and so on, then the total number of possibilities is the product of the number of each number of possibilities of each event.

m1m2m3mnm_1\cdot m_2\cdot m_3\cdots m_n

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