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?

Respuesta :

There are 26 letters in the alphabet, there are also 10 numbers 1-10. You multiply that and it would be 260.

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

What is exponents and powers?

When a number 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:

https://brainly.com/question/14881584

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