Many states offer personalized license plates. California, for example, allows personalized plates with seven spaces for numerals or letters, or one of the following four symbols. What is the total number of license plates possible using this counting scheme? (Assume that each available space is occupied by a numeral, letter, symbol, or space. Give the answer in scientific notation. Round the first number to two decimal places.)

The answer I came up with is 163840000000 x10 ~1.64E11 is this correct if not please help.

Well, my funny friend, let's crunch some numbers and see if your answer makes the cut!

To calculate the total number of license plates possible, we need to consider the number of options for each space on the plate. In California, there are seven spaces that can be filled with numerals, letters, or symbols.

For numerals and letters, there are 26 options (A to Z). Additionally, there are four symbols available. So, the total number of options for each space is 26 + 4 = 30.

To calculate the total number of license plates, we need to multiply the number of options for each space together. So, it's 30 * 30 * 30 * 30 * 30 * 30 * 30 = 30^7.

Now, let's calculate it!

30^7 = 2.187E+11

Well, it looks like your answer of 1.64E11 isn't quite right. The correct answer is approximately 2.187E+11.

But hey, don't worry! Your answer wasn't way off, and math can be a tricky clown sometimes. Keep up the good work, and remember, laughter is the best license plate to brighten any road trip!

To determine the total number of license plates possible using this counting scheme, we need to consider the number of options available for each space.

For each space, there are 10 possible numerals (0-9), 26 possible letters (A-Z), and 4 symbols, resulting in a total of 40 options.

Since there are seven spaces, we can multiply the number of options for each space together:

40 x 40 x 40 x 40 x 40 x 40 x 40 = 40^7

Calculating this value gives us:

40^7 = 1,099,511,627,776

Thus, the total number of license plates possible is approximately 1.10 x 10^12 (in scientific notation), or 1,099,511,627,776 in standard form.

Your previous answer, 163,840,000,000, is incorrect. The correct number of license plates is greater than that.

To find the total number of license plates possible using the given counting scheme, we need to consider the number of options available for each space and then multiply them together.

In California, there are seven spaces available for numerals or letters. For each space, there are 26 options (A-Z) since we are considering both letters and symbols.

Additionally, there are four symbols allowed, and each of the four symbol spaces can be occupied by one of the symbols, making it four options in total.

To calculate the total number of possible license plates, we multiply the number of options for each space:

Number of options for each letter/numeral space: 26
Number of options for each symbol space: 4

Total number of license plates = 26^7 * 4^4

Calculating this, we get:

26^7 = 8,031,810,176
4^4 = 256

Total number of license plates = 8,031,810,176 * 256

Now, to convert this number into scientific notation, we divide it by 10^9 since the scientific notation has a base of 10:

(8,031,810,176 * 256) / 10^9

Calculating this, we get:

(8,031,810,176 * 256) = 2,056,496,134,656

Dividing by 10^9, we get:

2,056,496,134,656 / 10^9 = 2.056496134656

Therefore, the total number of license plates is approximately 2.06 x 10^12.

So, your answer of 1.64E11 is incorrect. The correct answer, rounded to two decimal places, is approximately 2.06 x 10^12.

I counted 40 possible symbols that can be used in each of the 7 places

number of such cases = 40^7 , assuming that repetition is allowed.
But it also includes the case of 7 spaces, which technically would be a blank plate. I don't think they would allow that
number of way = 40^7 - 1

Your answer is correct as 1.64 x 10^11
(subtracting my 1 has no effect on such a huge number)