A state's license plates consist of four letters followed by three numerals, and 246 letter arrangements are not allowed. how many plates can the state issue?

The state will issue 4,56,97,354 plates

What is exponents and powers?

When anumber is multiplied by itself a finite number of times, the number being multiplied is called the base number, and the number of times it is being multiplied is called the exponent. Suppose a number is being multiplied by itself n number of times, then this expression is called the nth power of the given number.

• An exponent is the number of times a given number is being multiplied by itself.
• The expression when a number is being multiplied by itself n number of times is called the nth power of the given number.

Given:

Number of letters = 4

Number of numerals = 3

As 246 letter arrangements are not allowed.

So, we have total 26 letters.

and numbers from 0 to 9.

So, the number of plates  will be

= 26*26*26*26*10*10

=(26)^4 * (10)^2

= 45697600

Now, deducted those 246 letter arrangements which are not allowed

= 45697600 - 246

= 4,56,97,354

Hence, the state will issue 4,56,97,354 plates.

Learn more about this concept here:

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