Question

Standard automobile license plates in the country display two numbers fall by two letters followed by three numbers how many different standard plates are possible in this system

Answer 1

There is nothing stating that the letters and numbers can't be repeated, so all
26
letters of the alphabet and all
10
digits can be used again.

If the first is A, we have
26
possibilities:
AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have
26
possibilities:
BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.

There are
26
choices for the first letter and
26
choices for the second letter. The number of different combinations of
2
letters is:
26
×
26
=
676

The same applies for the three digits.
There are
10
choices for the first,
10
for the second and
10
for the third:

10
×
10
×
10
=
1000

So for a license plate which has
2
letters and
3
digits, there are:

26
×
26
×
10
×
10
×
10
=
676
,
000
possibilities.

Hope this helps.

Answer 2

Wow! What happened to that formatting?