A motorcycle licence plate has two letters followed by four numbers. How many plates can be made without duplicating? ( there are no plates with number zero)
Please give the full solution.
Dear Student!!!
@ Navin: Good work..!! Keep it up.
You have covered only one case (in which answer should be 6759324).
There can be two cases as follows:
Case 1: When letters are repeating
No. of ways of selecting of selecting number plates (including XX 0000) = 6760000
No. of ways of selecting plate with zero number= 26 × 26 × 1 = 676
Required no. of ways = 6760000 – 676 = 6759324
Case 2: When letters are distinct
26 25 10 10 10 10
(letters) (numbers)
No. of ways of selecting letters = 26 × 25 = 650
No. of ways of selecting numbers = 10 × 10 × 10 × 10 = 10000
No. of ways of selecting of selecting number plates (including XX 0000) = 650 × 10000
= 6500000
No. of ways of selecting plate with zero number = 26 × 25 × 1 = 250
Required no. of ways = 6500000 – 250 = 6499750
Cheers..!
