Respuesta :
Answer:
a) 67600000 possible plates
b) 19656000 possible plates where neither digit or letter are repeated
Step-by-step explanation:
The easiest way to solve this problem is seeing how many possibilities and there for each place in the license plate:
We have the following 7 places:
P1 - P2 - P3 - P4 - P5 - P6 - P7
The alphabet has 26 letters and there are 10 digits. So,
a) For each position there are the following possibilites
26 - 26 - 10 - 10 - 10 - 10 - 10
So in all, there are, 26*26*10*10*10*10*10 = 67600000 possible plates
b) Let's do the possibilites for each position again. Now, no letter or number can be repeated, so.
P1 is still 26. Now for P2, the letter in position P1 cannot be repeated, so there are only 25 possibilies. As for the digits, for P3, the first digit, there are still 10 possibilities. For P4, there are 9, since the digit in P3 cannot be repeated. For P5 there are 8, since P3 and P4 cannot be repeated... So there are the following number of possibilities:
26-25-10-9-8-7-6
In all, there are 26*25*10*9*8*7*6 = 19656000 possible plates where neither digit or letter are repeated.
The total number of choices for the 7-place license plates is when non of the number or letters are repeated is 19656000.
A.)
As we know that we have to choose a total of 7 places, out of these 7 places, the first 2 places are for letters and the other 5 for numbers.
The places that are for letters will have 26 choices each as the number can be repeated, similarly, the places that need number can be filled by the places in 0-9, therefore, a total of 10 different ways each
Thus, we can write,
The total number of choices for the 7-place license plates are,
= 26 x 26 x 10 x 10 x 10 x 10 x 10
= 676 x 100,000
= 6.76 x 10⁷
Hence, the number of ways 7-place license plates can be formed is 6.76 x 10⁷.
B.)
Now in the 7 place license number, the first two places are for number but such that the number can be repeated, therefore, the first place can be taken by any of the 26 letters, but the choices left with the second place will be 25 as one letter is been put at the first place, the same with happen for the numbers, the number of choices will be reduced, therefore,
The total number of choices for the 7-place license plates is when none of the numbers or letters are repeated,
Number of choices = 26 x 25 x 10 x 9 x 8 x 7 x 6
Number of choices = 19656000
Hence, the total number of choices for the 7-place license plates is when none of the numbers or letters are repeated is 19656000.
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