Question

What if the authorities of Combinatoria degree that (1) the three letters must be distinct, (2) the four digits must also be distinct, and (3) the first of the four digits cannot be 0. Now how many distinct license plates are there?

Answer 1

Explanation:

Given that (1) the three letters must be distinct, (2) the four digits must also be distinct, and (3) the first of the four digits cannot be 0.

Out of 26 letters 3 different letters can be arranged if order matters in 26P3 ways

i.e.
`26(25)(24) =15600`

4 digits with I digit non zero

So I zero can be selected in 9 ways excluding 0, 3rd digit in 9 ways excluding I digit, 2nd in 8 and 3rd in 7

No of ways
`= 9(9)(8)(7) =4536`

Total no of ways
`= 4536(15600) =70761600`