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
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.
To find out how many different standard license plates are possible in this system, we need to calculate the total number of combinations.
In this case, the license plates consist of two numbers followed by two letters and finally three numbers. Let's break it down into different parts:
1. For the first set of two numbers: Assuming there are no restrictions or repetitions allowed, we have 10 possible choices for each position (0-9). Therefore, there are 10 × 10 = 100 possible combinations.
2. For the set of two letters: Assuming we are using all the letters of the alphabet (no restrictions or repetitions allowed), we have 26 possible choices for each position. Therefore, there are 26 × 26 = 676 possible combinations.
3. For the final set of three numbers: Using the same assumption of no restrictions or repetitions allowed, we have 10 possible choices for each position. Therefore, there are 10 × 10 × 10 = 1000 possible combinations.
To calculate the total number of possible license plates, we multiply the number of combinations for each part:
Total number of plates = (number of combinations for numbers) × (number of combinations for letters) × (number of combinations for numbers)
= 100 × 676 × 1000
= 67,600,000
Therefore, there are 67,600,000 different standard license plates possible in this system.