How do I answer these questions?

Question

. A state license plate consists of 1 letter followed by 5 digits.

 

a. How many different license plates can be made?​​​​​​​15a. _________

 

b. If no digit could be repeated, how many possible license plates would there be?​​​b. ___________

 

c. A witness to a crime saw the first letter and first three digits of a license plate correctly as A463​ c. ___________

but could not see the last two digits. How many license plates could start with A463?

Answer 1

a. How many different license plates can be made?​​​​​​​

There are 26 choices for the letter (A to Z)

There are 10 choices for the first digit (0 to 9)

There are 10 choices for the second digit

There are 10 choices for the third digit.

There are 10 choices for the fourth digit.

There are 10 choices for the fifth digit.

Multiply to get the total ways.

26 x 10 x 10 x 10 x 10 x 10

Answer:

2,600,000 possible license plates

 

b. If no digit could be repeated, how many possible license plates would there be?​​​

There are 26 choices for the letter (A to Z)

There are 10 choices for the first digit (0 to 9)

There are 9 choices for the second digit (can't repeat).

There are 8 choices for the third digit.

There are 7 choices for the fourth digit.

There are 6 choices for the fifth digit.

Multiply to get the total ways.

26 x 10 x 9 x 8 x 7 x 6

Answer:

786,240 possible license plates

 

c. A witness to a crime saw the first letter and first three digits of a license plate correctly as A463​

but could not see the last two digits. How many license plates could start with A463?

The first part of the plate is found.

There are 7 choices for the fourth digit (since we've already used 3 digits)

There are 6 choices for the fifth digit (since we've already used 4 digits)

Multiply to get the total ways.

7 x 6

Answer:

42 license plates starting with A463. (Assuming the numbers are not repeated)