Respuesta :
The probability that all symbols are different is 0.45 and the probability that all all symbols are different and the first number is the largest among the numbers is 0.11.
There are three places for alphabets, which can be filled by any one of the 26 letters. So the total possible ways of selecting 3 letters is 26³.
There are four places for alphabets, which can be filled by any one of the 10 digits. So the total possible ways of selecting 4 numbers is [tex]10^{4}[/tex].
So, the total possible ways of selecting 3 alphabets and 4 numbers for license plates is 26³ × [tex]10^{4}[/tex] = 175760000.
(a) The probability that all symbols are different.
The three letters can be selected in 26! ways = 26 × 25 × 24 = 15600
Similarly, the four numbers can be selected in 10! ways = 10 × 9 × 8 × 7 = 5040
Therefore, the probability that all symbols are different is
= 15600 × 5040 / 175760000
= 0.45 approximately
(b) The probability that all symbols are different and the first number is the largest among the numbers.
The probability that first number is largest among the numbers is = 3!/4! = 1/4
The probability that all symbols are different is 0.45 approximately
Therefore, the required probability is
= 1/4 of 0.45
= 0.11 approximately.
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