Question

How many different 4 digit number licence plates can be made if

i. Repetition is not allowed

ii. Repetition is allowed

Answer 1

Licence plate contains 2 letters and 4 digits.

(i)
No of letters =2
There are 26 letters in english.
so,with no repetition
⇒ There can be 26×25=650
(26---> a letter from 26 letters is used as first letter.
so , 25 letters are remaining unused.
25---> a letter from remaining 25 letter is used as second letter)

So, 650 Combinations are possible with 2 letters.


No of digits =4
There are total of 10 digits in maths.
Hence the no of 4 digit nubers possible without repetitions is
⇒10×9×8x7
⇒5040.
so 5040 combinations are possible with 4 digits


Total no of ways of making the plates with digits and letters =650 x 5040 =3276000

(ii)
There are 26 letters.
Taking 2 letters,
26 x 26 combinations are possible with repetition.
(Note: it is 26x25 in (i) case.because, letter used as first letter cannot be used as second letter).
Therefore , combinations possible with two letters=26x26 =676.

There are total of 10 digits available in maths.

No of combinations usng 4 digits with repetition = 10 x 10 x 10 x10 =1000
(all 4 places in number can be filled with any digit in maths).

Therefore total no of combinations with letters and digita with repetition
= 676 x 10000 = 6760000.

Thanks