How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?

# How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?

J
240 points

a) How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?

b) Repeat part (a) under the assumption that no letter or number can be repeated in a single license plate.

How many
jeffp

8.7k points

part (a) There are 26 letters in the alphabet and 10 possible numbers to use. It is a counting problem and hence,

$$26^2 10^5 = 67600000$$

part (b) Repetitions are not allowed so for the first choice we have 26 letters to choose from, and then 25 letters.. Likewise for the numbers we can choose 10 numbers for the 3rd position, then 9 numbers, and so on...

$$26 \cdot 25 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6= 19656000$$

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