Q:

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?

Accepted Solution

A:
Answer:2,948,400Step-by-step 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