Air draft

The numbers 1,2,3,4,5 are written on five tickets on the table. Air draft randomly shuffled the tickets and composed a 5-digit number from them. What is the probability that he passed:
and the largest possible number
b, the smallest possible number
c, a number divisible by five
d, even number
e, odd number
f, a number divisible by three
g, a number divisible by nine

Correct answer:

a =  0.0083
b =  0.0083
c =  0.2
d =  0.4
e =  0.6
f =  1
g =  0

Step-by-step explanation:

$a=\frac{1}{5!}=\frac{1}{120}=0.0083$

$b=a=\frac{1}{120}=0.0083$

$c=\frac{4\cdot 3\cdot 2\cdot 1\cdot 1}{5!}=\frac{1}{5}=0.2$

$d=\frac{4\cdot 3\cdot 2\cdot 1\cdot 2}{5!}=\frac{2}{5}=0.4$

$e=\frac{4\cdot 3\cdot 2\cdot 1\cdot 3}{5!}=\frac{3}{5}=0.6$

$$\begin{gathered} c=1+2+3+4+5=15 \\ {c}_2=1+5=6 \\ f=\frac{5!}{5!}=1 \end{gathered}$$

$$\begin{gathered} g_1=c/3=15/3=5 \\ g=0 \end{gathered}$$

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