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  • Four letters and four digits make up a number plate. The letters must come from the set "A, B, C, D, E, F" and the digits must come from the set "0, 1, 2, 3, 4" if rep

Four letters and four digits make up a number plate. The letters must come from the set "A, B, C, D, E, F" and the digits must come from the set "0, 1, 2, 3, 4" if repetition is permitted. How many different types of number plates are there?

Option: 1

620000


Option: 2

710000


Option: 3

920000

 


Option: 4

810000


Answers (1)

best_answer

Given that,

The number plate consists of 4 letters and 4 digits.

The first three letters will be from A, B, C, D, E, and F.

The last three letters will be from 0, 1, 2, 3, and 4.

There are 6 choices for each of the 4 letters, so the number of different ways to choose the letters is given by,

6 \times 6 \times 6 \times 6=1296

Similarly, there are 5 choices for each of the 4 digits, so the number of different ways to choose the digits is given by,

5 \times 5 \times 5 \times 5=625

The number of possible number plates can be calculated using the multiplication principle because the options for the letters and digits are independent.

Thus,

\begin{aligned} &\text{The total number of possible number plates }= \text{ The number of choices for the letter} \times \text{ The number of choices for the digits }\\ & N=1296 \times 625 \\ & N=810000 \end{aligned}

 

 

 

 

 

 

Therefore, the number of ways to form the number plate is 810000.

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manish

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