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[SOLVED] determine how many licence plates would cost $100

Dhamnekar Winod

Active member
Nov 17, 2018
115
In a certain state of a certain country, each vehicle licence plates have exactly three letters followed by three digits. We are told that to produce such a licence plate, it costs $n for each digit n>0 and $10 for each digit 0. For letters the cost is proportional to the position of the letter in the alphabet, namely \$1 for A, \$2for B, so on and so forth, upto $26 for Z.

Now, how to determine how many licence plates would cost $100?

Answer:- I don't understand how to answer this question. I think linear programming will help here.
 
Last edited:

michaelalex

New member
Apr 11, 2020
1
This question seems to be difficult and maybe linear programming can help here.
 

Dhamnekar Winod

Active member
Nov 17, 2018
115
In a certain state of a certain country, each vehicle licence plates have exactly three letters followed by three digits. We are told that to produce such a licence plate, it costs $n for each digit n>0 and $10 for each digit 0. For letters the cost is proportional to the position of the letter in the alphabet, namely \$1 for A, \$2for B, so on and so forth, upto $26 for Z.

Now, how to determine how many licence plates would cost $100?

Answer:- I don't understand how to answer this question. I think linear programming will help here.

Hello,
After working on finding out the answer to this question, eventually i suceeded. The answer to this question is 1287 licence plates would cost \$100.

Justification to the answer:-

The maximum possible cost is \$108 of the licence plate having ZZZ 000. Finding the number of licence plates having the cost of \$100 is equivalent to finding how many ways 8 indistinguishable balls can be put into 6 distinguishable cells. So $\binom{n+r-1=13}{r=8}=1287 $ licence plates.