How many 4-character license plates are possible with 2
letters from the alphabet followed by 2 digits, if repetitions
are allowed? if repetitions are not allowed?
a) 26x26x10x10
b) 26x25x10x9
To find the number of possible 4-character license plates with 2 letters from the alphabet followed by 2 digits, we can first determine the number of options for each character placement.
If repetitions are allowed:
For the first and second character positions, we have 26 options each (since there are 26 letters in the alphabet). For the third and fourth character positions, we have 10 options each (since there are 10 digits from 0 to 9).
Therefore, to find the total number of possible license plates with repetitions allowed, we multiply the number of options for each position:
26 options for the first position * 26 options for the second position * 10 options for the third position * 10 options for the fourth position = 67600 possible license plates.
If repetitions are not allowed:
For the first character position, we have 26 options. For the second character position, we have 25 options (since one letter has already been used and cannot be repeated). For the third and fourth character positions, we have 10 options each.
Therefore, to find the total number of possible license plates without repetitions allowed, we multiply the number of options for each position:
26 options for the first position * 25 options for the second position * 10 options for the third position * 10 options for the fourth position = 65,000 possible license plates.