MHB Determine how many licence plates would cost $100

[WMDhamnekar]

In a certain state of a certain country, each vehicle license plates have exactly three letters followed by three digits. We are told that to produce such a license 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 license plates would cost $100?

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

 

[michaelalex]

This question seems to be difficult and maybe linear programming can help here.

 

[WMDhamnekar]

In a certain state of a certain country, each vehicle license plates have exactly three letters followed by three digits. We are told that to produce such a license 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 license 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 license plates would cost \$100.

Justification to the answer:-

The maximum possible cost is \$108 of the license plate having ZZZ 000. Finding the number of license 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 $ license plates.