A license

A licence plate has three letters followed by four digits. Letters may not be repeated, but digits may be repeated. If plates are issued at random, what is the probability that the three letters are in alphabetical order and the four digits are consecutive?

Final Answer:

p =  3.0E-5

Step-by-step explanation:

$$\begin{gathered} n_1=26\cdot 25\cdot 24=15600 \\ {n}_2=10^4=10000 \\ n=n_1\cdot n_2=15600\cdot 10000=156000000 \\ {a}_1=25\cdot 1\cdot 1=25 \\ {b}_1=9\cdot 1\cdot 1\cdot 10+10\cdot 9\cdot 1\cdot 1=180 \\ p=\frac{a_1\cdot b_1}{n}=\frac{25\cdot 180}{156000000}=3.0\cdot 10^{-5} \end{gathered}$$

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