In Oregon, standard license plates consists of 3 letters (there are 26 letters i
ID: 3228048 • Letter: I
Question
In Oregon, standard license plates consists of 3 letters (there are 26 letters in the alphabet in the alphabet) followed by 3 digits (0, 1, ...., 9). Assume there are no other restrictions. A witness to a hit-and-run accident told the police that the 1^st letter of the vehicle's license plate was a "Z" and the second letter was a vowel (A, E, I, O, or U). The witness also noticed that all three of the digits different. How many license plates (Oregon standard issue) meet the witness's description? A train is hauling 60 containers, 45 of which are for Seattle. 15 are destined for V Vancouver. if three containers are randomly selected. What is the probability that two of the three are destined for Seattle?Explanation / Answer
THE LICENSE PLATE HAS 3 LETTERS PLACE(A1,A2,A3) AND 3 NUMBER PLACE(L1,L2,L3)
A1 A2 A3 L1 L2 L3
Z 5 20 10 9 8
A1= Z ALPHABET IS FIXED
A2= ANY ONE OF THE 5 VOWEL CAN BE PRESENT
A3: ANY ALPHABET FROM REMAINING 20 CONSONANTS /ALPHABET
L1:ANY ONE FROM 10 NUMBER
L2 : NUMBER FORM REMAINING 9 NUMBERS
L3: FROM REMAINING 8 NUMBERS
TOTAL LICENSE PLATE PERMUTATIONS: 20*5*10*9*8=72000
q4: TOTAL NUMBER OF CONTAINERS: 60
SEATLLE=45 VANCOVER=15
SINCE RANDOMLY THREE ARE PICKED ONE BELONGS FROM VANCOVER N OTHER TWO BELONGS FROM SEATLLE LOT
PROBABILITY: picking two from seattle*picking one from vanover/total picks from all ie three
=> (15C1 *45C2)/60C3 using formula: nCr =n!/(n-1!r!)
calculate: 15*990/68440 =0.216 =21.6%
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