Eight children of different ages are arranged at random in a line. Find how many different arrangements are possible if none of the three youngest children are beside one another.
David picks $5$ chocolates from $6$ different dark chocolates, $4$ different white chocolates and $1$ milk chocolate. He has to choose at least one of each type. Find the number of different selections he can make.
Chelsea’s computer password contains 4 characters in a fixed order. The characters are selected from the following: the 26 capital letters A to Z; the 9 digits 1 to 9; the 5 symbols $\#, \sim, *, ?, !$ . The password must contain at least one capital letter, at least one digit and at least one symbol. No character may be used more than once. Find the number of different passwords that Chelsea can make.