License plates in California consist of a number, followed by three letters, and

Question

License plates in California consist of a number, followed by three letters, and then by three numbers. How many possible license plates are possible if no repetitions are allowed?
How many possible license plates are possible if repetitions are allowed? License plates in California consist of a number, followed by three letters, and then by three numbers. How many possible license plates are possible if no repetitions are allowed? License plates in California consist of a number, followed by three letters, and then by three numbers. How many possible license plates are possible if no repetitions are allowed?
How many possible license plates are possible if repetitions are allowed?

Explanation / Answer

Here number plates are like in the fomat i.e 1ADF347

(i) Now we know the no repetititons are allowed

so there are 10 eligible number at first digit, for letters there are 26 alphabets present.

so total combinations = 10 * 26 * 25 * 24 * 9 * 8 * 7 = 78,624,000

(ii) Now repetitions are allowed so each number has 10 possibilites and each digits have 26 possibilities

so total possible plates are = 10 * 26 * 26 * 26 * 10 * 10 * 10 = 175,760,000

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