Number plates in an Arab country consist of 3 letters (chosen from a specified set of 20 letters from the Arabic alphabet) and 4 digits (from 0 to 9).
⦁ Find the probability of a plate having identical letters.
⦁ Find the probability of a plate having identical digits.
⦁ Find the probability of a plate having consecutive digits.
1:20⋅120⋅120⋅120=0.00252:10⋅110⋅110⋅110⋅110=0.0013:The 4digits in ascending order can start from 0,1,2,3,4,5That is 6waysThere are 2ways to choose order (ascending or descending)Total 6⋅2=12ways of 104=10000variants of digitsThe probability is1210000=0.00121:\\20\cdot \frac{1}{20}\cdot \frac{1}{20}\cdot \frac{1}{20}=0.0025\\2:\\10\cdot \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{1}{10}=0.001\\3:\\The\,\,4 digits\,\,in\,\,ascending\,\,order\,\,can\,\,start\,\,from\,\,0,1,2,3,4,5\\That\,\,is\,\,6 ways\\There\,\,are\,\,2 ways\,\,to\,\,choose\,\,order\,\,\left( ascending\,\,or\,\,descending \right) \\Total\,\,6\cdot 2=12 ways\,\,of\,\,10^4=10000 variants\,\,of\,\,digits\\The\,\,probability\,\,is\\\frac{12}{10000}=0.00121:20⋅201⋅201⋅201=0.00252:10⋅101⋅101⋅101⋅101=0.0013:The4digitsinascendingordercanstartfrom0,1,2,3,4,5Thatis6waysThereare2waystochooseorder(ascendingordescending)Total6⋅2=12waysof104=10000variantsofdigitsTheprobabilityis1000012=0.0012
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