Question

5. PA license plates have 3 letters followed by 4 numbers.

Answer 1

Answer:

A. 175,760,000

B. 156,000,000

Step-by-step explanation:

For part A:

There are 26 letters in the alphabet.  Therefore, if there are 3 spots to use 26 letters, that is represented as $26^3$.  As for numbers, there are 10 digits from 0-9.  So if there are 4 spots for numbers, the total possible number of sequences is $10^4$.  So you simply multiply $26^3$ and $10^4$ to get 175,760,000 possible combinations.

For part B:

If the same letter can't be repeated, instead of using an exponent, we have to use a factorial, but only for the 3 digits required in the license plate.  These are called permutations and can be expressed as $_2_6P_3$, which is the same as saying 26 x 25 x 24.  Since there is no change to number of numbers, that remains the same.

$_2_6P_3 * 10^4 =26*25*24*10^4=156,000,000$