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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:

Respuesta :

Edufirst

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
fichoh

Using the multiplication operation, the number of unique license plates the new country can support would be 2 raised to the power of 7 [tex]2^{7} = 128 [/tex] license plates

  • The length of digits on each license plates = 7

Since the license plates uses binary numbers ; then the only possible digits on the plates would be 0 and 1

To obtain the total number of possible unique plates :

  • [tex](Number \: of \: binary \: digits)^{number \: of\:digits \: per \: plate} [/tex]

Therefore, the total number of unique license plates are : [tex]2^{7} = 128 [/tex]

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