Daemi 1 / Problem 1 (20%) Bilnumer skulu hafa 5 stafi. Fyrst koma 2 bokstafir, sidan kemur bokstafur eda tolustafur o loks koma 2 tolustafir. Gerum rad fyrir 30 bokstofum i stafrofinu og ao oll slik bilnumer se leyfileg (t.d. ABC43, AB513, WWW07 og TB000). ("A car registration number consists of symbols. First there are 2 letters, the third symbol is a letter or a digit and finally there an 2 digits. Assume that there are 30 different letters and that all such registration numbers an valid (e.g. ABC43, AB513, WWW07 and TB000)") a) (6%) Hve morg mismunandi bilnumer eru til? Setjio upp svario og reiknid ut ur bvi. ("Ho many car registration numbers are there? Show a formula and compute a final answer." b) (7%) I hve morgum bilnumerum kemur hvorki fyrir bokstafurinn X ne tolustafurinn 8 Setjio upp svario og reiknid ut ur bvi. ("How many car registration numbers contai neither the letter X nor the digit 8? Show a formula and compute a final answer.") b) (7%) I hve morgum bilnumerum kemur fyrir bokstafurinn R, en hvorki bokstafurinn ne tolustafurinn 8? Setjio upp svario og reiknid ut ur pvi. ("How many car registration numbers contain the letter R, but neither the letter X nor the digit 8? Show a formul and compute a final answer.")