(a(i))[2]
Determine how many distinct numbers may be formed by rearranging all nine digits of the number $223\,677\,888$ with no extra conditions.
(a(ii))[4]
Determine how many distinct numbers may be formed by rearranging all nine digits of $223\,677\,888$ so that the resulting number is even.
(b)[5]
Sandra wants to purchase some smartphone applications (apps), but she can afford only $5$ apps altogether. There are $3$ train apps, $6$ social network apps and $14$ games apps to choose from. Sandra requires at least $1$ app from each type. Find the number of different selections of $5$ apps that Sandra could make.