How many six-digit license plates can be manufactured if no license plate number begins with 0

Question

I'm not sure how to exclude just one number would it just be p(6,5). ?

Answer 1

The first digit may be 1-9;  subsequent digits may be 0-9.  Digits may be repeated.

 

This means 9*10*10*10*10*10 possibilities.  That is:  9*10⁵ = 900,000.

 

Think of a counter (like an odometer) that has the following digits on the dials:

  1  0  0  0  0  0

  2  1  1  1  1  1

  3  2  2  2  2  2

  4  3  3  3  3  3

  5  4  4  4  4  4

  6  5  5  5  5  5

  7  6  6  6  6  6

  8  7  7  7  7  7

  9  8  8  8  8  8

      9  9  9  9  9

Rotate ones place, then tens place, etc.  That gives numbers from 100000 to 999999.

   How many?    999999 - 100000 + 1 = 900,000

Answer 2

assuming repetition

0,1,2,3,4,5,6,7,8,9

first place you choose from only 9 digits (0 excluded)

the other five places you choose from 10 digits

9*10*10*10*10*10=900,000 plates

Answer 3

For digits 2 through 6: ₁₀C₅

Then multiply that number by 9 (the the first digits 1 through 9)