How many 4-character license plates are possible with 2 letters from the alphabet followed by 2 digits, if repetitions are allowed? And no repetitions are allowed?
Answer: If repetitions are allowed: 26*26*10*10=67,600
No repetitions are allowed: 26*25*10*9=58,500
Is this correct?
Thanks.
correct.
Yes, your answers are correct.
To find the number of possibilities for a 4-character license plate with 2 letters from the alphabet followed by 2 digits, we need to consider two scenarios - repetitions allowed and no repetitions allowed.
Repetitions allowed:
In this case, we can have any letter or digit repeated in the license plate. Each position in the license plate can have 26 possible letters (since there are 26 letters in the alphabet) and 10 possible digits (since there are 10 digits). Therefore, the total number of possibilities is obtained by multiplying the number of choices for each position:
26 (choices for the first letter) * 26 (choices for the second letter) * 10 (choices for the first digit) * 10 (choices for the second digit) = 67,600 possibilities.
No repetitions allowed:
In this case, once a letter or digit is used, it cannot be reused in any other position. The calculation for the number of possibilities is similar, but we have fewer choices for each position as we need to subtract the previously selected characters:
26 (choices for the first letter) * 25 (choices for the second letter) * 10 (choices for the first digit) * 9 (choices for the second digit) = 58,500 possibilities.
So, your answers of 67,600 with repetitions allowed and 58,500 with no repetitions allowed are correct.