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Now, how to determine how many licence plates would cost $100? Answer:- I don't understand how to answer this question. I think linear programming will help here. Last edited: #### michaelalex ##### New member This question seems to be difficult and maybe linear programming can help here. #### Dhamnekar Winod ##### Active member In a certain state of a certain country, each vehicle licence plates have exactly three letters followed by three digits. We are told that to produce such a licence plate, it costs$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.

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.