A license plate is any sevencharacter string of digits from

A license plate is any seven-character string of digits from 0-9 and/or uppercase letters, where you can repeat digits and/or letters.

a) How many license plates start with an odd digit?

b) How many license plates are either all digits or all letters?

Solution

a)

There are 26+10 = 36 choices for each of the 7 characters.

There are 5 odd digits.

Thus, there are 5*36*36*36*36*36*36 = 10883911680 such plates [ANSWER]

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b)

There are 10*10*10*10*10*10*10 = 10 000 000 plates with all digits.

There are 26*26*26*26*26*26*26 = 8031810176 plates with all letters.

Hence, a total of 8031810176 + 10000000 = 8041810176 such plates. [ANSWER]