Question

A liscense plate consists of 2 letters followed by 4 digits. If the two letters must be different and the first digit cannot be 0, how many liscense plates are possible?

Answer 1

`S = 5,850,000` possible plates

Explanation:

There are 26 letters in the abcedary and 10 possible digits

Then we know that the first 2 letters must be different and that the first digit must not be zero.

So we know that for the first letter there are 26 possibilities

For the second letter there are 25 possibilities, because it should not be equal to the first

For the first digit there are 9 possibilities (because it must be non-zero)

For the 3 following digits there are 10 possibilities for each one.

Then the sample space is composed of the product of the possible values for each term of the plate.

`S = 26 * 25 * 9 * 10 * 10 * 10`

`S = 5,850,000` possible plates

Answer 2

2,948,400

Explanation:

For the first letter, there are possibility of putting 26 different letter from the alphabet.

For the second letter, there are possibility of putting 25 different letters from the alphabet (since repetition is not allowed from first digit)

Now,

For first digit, there is possibility of 9 digits, since 0 is NOT ALLOWED.

For second digit, there is possibility of 9 digits, since 0 IS ALLOWED BUT repetition of first digit is not allowed.

For third digit, there is possibility of 8 digits, since 2 are taken in first 2 slots and repetition is not allowed.

For fourth digit, there is possibility of 7 digits, since 3 are taken in first 3 slots and repetition is not allowed.

Now we multiply all the possibilities to get the number of license plates possible.

26 * 25 * 9 * 9 * 8 * 7 = 2,948,400