Question

A bunch of computer scientists take over an island and start their own country. They want the license plates to use binary numbers. There's space for 7 digits on each license plate and the first plate starts at 000000000000000000000.
How many unique license plates can their country support? Answer in decimal:

Answer 1

Answer:

• Their country can support   128   unique license plates

Explanation:

Since there is space for 7 digits on each license plate, the first plate starts at 0000000 (seven 0).

Binary numbers contain only the digits 0 and 1.

Thus, there are only two possibilities for each digit.

Using the multiplication counting principle, the number of total different binary numbers, with seven digits is 2 multiplied seven times:

• 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷ = 128 ← answer