There are [tex]{}_5P_4=5!\dbinom54=\dfrac{5!}{(5-4)!}=120[/tex] ways of making four-digit codes from the five available odd numerals (1, 3, 5, 7, 9) without replacement. Without any restrictions aside from no replacement, there are [tex]{}_{10}P_4=10!\dbinom{10}4=\dfrac{10!}{(10-4)!}=5040[/tex] possible codes that can be made. So the probability of randomly choosing a code made up only odd digits is
[tex]\dfrac{120}{5040}[/tex]
which means the probability of this not occurring is
[tex]1-\dfrac{120}{5040}\approx0.976[/tex]
