Items NOT together (general separation)

3

1. How many different arrangements are there of the 8 letters in the word RELEASED?
2. How many different arrangements are there of the 8 letters in the word RELEASED in which the letters LED appear together in that order?
3. An arrangement of the 8 letters in the word RELEASED is chosen at random. Find the probability that the letters A and D are not together.

7

1. Find the number of different arrangements of the 10 letters in the word CASABLANCA in which the two Cs are not together.
2. Find the number of different arrangements of the 10 letters in the word CASABLANCA which have an A at the beginning, an A at the end and exactly 3 letters between the 2 Cs .
   Five letters are selected from the 10 letters in the word CASABLANCA.
3. Find the number of different selections in which the five letters include at least two As and at most one C.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.

7 Nine cards, each of a different colour, are to be arranged in a line.

1. How many different arrangements of the 9 cards are possible? The 9 cards include a pink card and a green card.
2. How many different arrangements do not have the pink card next to the green card? Consider all possible choices of 3 cards from the 9 cards with the 3 cards being arranged in a line.
3. How many different arrangements in total of 3 cards are possible?
4. How many of the arrangements of 3 cards in part (iii) contain the pink card?
5. How many of the arrangements of 3 cards in part (iii) do not have the pink card next to the green card?

2 Fahad has 4 different coloured pairs of shoes (white, red, blue and black), 3 different coloured pairs of jeans (blue, black and brown) and 7 different coloured tee shirts (red, orange, yellow, blue, green, white and purple).

1. Fahad chooses an outfit consisting of one pair of shoes, one pair of jeans and one tee shirt. How many different outfits can he choose?
2. How many different ways can Fahad arrange his 3 jeans and 7 tee shirts in a row if the two blue items are not next to each other? Fahad also has 9 different books about sport. When he goes on holiday he chooses at least one of these books to take with him.
3. How many different selections are there if he can take any number of books ranging from just one of them to all of them?

7

1. 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.
2. 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.
3. 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 group consists of 5 men and 2 women. Find the number of different ways that the group can stand in a line if the women are not next to each other.