CAIE A-Level Mathematics 5.2.2 Restricted Arrangements

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

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: 6]

In a group of 25 athletes, there are 8 sprinters, 5 hurdlers and 12 throwers.

(a)

How many different arrangements of the 8 athletes are there if the 3 hurdlers do not stand all together?

[ 3 ]

(b)

How many different arrangements of the 8 athletes are there in which there are at least two athletes between any two hurdlers?

[ 3 ]