Answer:
a. 67600000
b. 0.0001396
c. 0.001479
Step-by-step explanation:
a. Since it is a permutation with repetition the formula is:
[tex]n^r[/tex]
Where [tex]n[/tex] is the number of optionss, here you will use [tex]n_1=10[/tex] and [tex]n_2=26[/tex], one for the numbers and the other for the letters. The exponent [tex]r[/tex] corresponds to how many times you have to choose a number (5 times) or a letter (two times because the first letter is always the same), then:
[tex]n_1^5*n_2^2=10^5*26^2=100000*676=67600000=6.76\times10^7[/tex]
b. The probability of getting that exactly serial number is 1 divided by the total of possibilities:
[tex]P_b=\frac{1}{6.76\times10^7}=0.0001396=1.396\times10^{-4}[/tex]
C. The probability is the number of serials ending with AA divided by the total. The serial ending with AA can have any numbers then [tex]n=10[/tex] and [tex]r=5[/tex]
[tex]n^r=10^5=100000=1\times10^5[/tex]
[tex]P_c=\frac{1\times10^5}{6.76\times10^7}=0.001479=1.479\times10^{-3}[/tex]
