CAIE A-Level Mathematics 5.2.2 Restricted Arrangements

Practise line arrangements with repeated objects, blocks, gaps, fixed positions and adjacency or separation restrictions.

Exam points

divide by repeated-object factorials when counting distinct word arrangements
treat objects kept together as a block, then remove cases violating another restriction
place separated objects into valid gaps or count positions satisfying a fixed distance

[Maximum number: 4]

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.

(a)

How many different arrangements of the 9 members are possible in which Raman will be at the centre of the line?

[ 1 ]

(b)

How many different arrangements of the 9 members are possible in which Raman and Sanjay are not next to each other?

[ 3 ]

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5.2.2—Arrangement restrictions question 1

Question (a)

Question (b)