Practise counting arrangements and selections with repeated objects, fixed positions, adjacency restrictions and case conditions by choosing permutations or combinations correctly.
Raman and Sanjay are members of a quiz team which has 9 members in total. Two photographs of the quiz team are to be taken.
For the first photograph, the 9 members will stand in a line.
How many different arrangements of the 9 members are possible in which Raman will be at the centre of the line?
How many different arrangements of the 9 members are possible in which Raman and Sanjay are not next to each other?
For the second photograph, the members will stand in two rows, with 5 in the back row and 4 in the front row.
In how many different ways can the 9 members be divided into a group of 5 and a group of 4?
In a restaurant, the tables are rectangular. Each table seats four people: two along each of the longer sides of the table (see diagram). Eight friends have booked two tables, X and Y. Rajid, Sue and Tan are three of these friends.
When the friends arrive at the restaurant, Rajid and Sue now decide to sit at table X on the same side as each other. Tan decides that he does not mind at which table he sits.
The eight friends will be divided into two groups of 4, one group for table X and one group for table Y.
Find the number of ways in which this can be done if Rajid and Sue must sit at the same table as each other and Tan must sit at the other table.
Find the number of different seating arrangements for the 8 friends.
As they leave the restaurant, the 8 friends stand in a line for a photograph.
Find the number of different arrangements if Rajid and Sue stand next to each other, but neither is at an end of the line.