Question

Furthermore, each license plate string must contain exactly 8 distinct characters (including the space character). For example, CMSC250 is not a valid license plate string, but ’CM8Z 2S0’ and ’BIGCARSZ’ are. How many license plate strings are possible?

Answer 1

1,556,675,366,400

Explanation:

There are 37 possible characters, of which 8 can be chosen. Order matters, so the number is ...

37P8 = 1,556,675,366,400

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This number includes 84,144,614,400 strings in which the space character is either first or last. Such strings may be ruled invalid because they are indistinguishable from 7-character strings.

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nPk = n!/(n-k)! . . . . the number of permutations of n things taken k at a time

The 37 allowed characters are the 26 letters of the alphabet, 10 digits, and 1 space character.