Question

The new motorcycle license plate format issued by the Land Transportation Office consists of two letters from the English alphabet and four digits from 0 to 9. A witness of a riding-in-tandem crime reported to the police that he can only remember the first two letters of the license plate, E E _ _ _ _. He was also certain that the four digits of the license plate are distinct, and 1 is not included if 4 is included, and vice versa. If the police officer searches for the motorcycle, how many possible license plate numbers does he have to consider?

Calling ganeshie8 hihi. :)

Answer 1

if there is a 1 included then there are 8 numbers (0,2,3,5,6,7,8,9) from which any 3 can be taken That is 8P3 possible permutations.

Answer 2

= 8*7*6 = 336 ways

also the 1 can be in any of 4 positions so total ways = 4 * 336

The same reasoning can be applied if there is a 4 in the last 4 numbers

Answer 3

So, the total number of license numbers is,

(4 x 336) x 2 + 8P4 = 4368

Answer 4

4368 is right!

Answer 5

Another way to work it is :
Total four digit numbers = 10P4
Four digit numbers with both 4 and 1 = 4P2*8P2

So the desired number of license number = 10P4 - 4P2*8P2

Answer 6

I dont follow that why 8P4?.

Answer 7

i'm not saying you guys are wrong. Stats is not my strong point.

Answer 8

number of four digit numbers "without" 4 or 1 = 8P4

Answer 9

I got 8P4 from the case where 1 and 4 are both not included. So i guess that's why

Wow Mr. Ganeshie, we got the same answer. But can you please explain? Haha. I did not kind of understand it

Answer 10

oh yes - I assumed that 1 or 4 had to be there - but thats not the case of course.

Answer 11

which part you're looking at ? :)

Answer 12

Mr ganeshie, do you know any online sites where I can study combinatorics or any other branch of mathematics? High school level >:)