(a) Eight children of different ages stand in a random order in a line. Find the number of different ways this can be done if none of the three youngest children stand next to each other. (b) David chooses 5 chocolates from 6 different dark chocolates, 4 different white chocolates and 1 milk chocolate. He must choose at least one of each type. Find the number of different selections he can make. (c) A password for Chelsea's computer consists of 4 characters in a particular order. The characters are chosen from the following. • The 26 capital letters A to Z • The 9 digits 1 to 9 • The 5 symbols # ~ * ?! The password must include at least one capital letter, at least one digit and at least one symbol. No character can be repeated. Find the number of different passwords that Chelsea can make.

1. (a)Eight children of different ages stand in a random order in a line. Find the number of different ways this can be done if none of the three youngest children stand next to each other.[3]
2. (b)David chooses 5 chocolates from 6 different dark chocolates, 4 different white chocolates and 1 milk chocolate. He must choose at least one of each type. Find the number of different selections he can make.[4]
3. (c)A password for Chelsea's computer consists of 4 characters in a particular order. The characters are chosen from the following. • The 26 capital letters A to Z • The 9 digits 1 to 9 • The 5 symbols # ~ * ?! The password must include at least one capital letter, at least one digit and at least one symbol. No character can be repeated. Find the number of different passwords that Chelsea can make.[4]