## Exam-Style Question on Combinatorics## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 636. This question is similar to one that appeared on an IB AA Higher paper in 2022. The use of a calculator is allowed.

Fifty years ago there was a zoo where animals were housed in cages. There were eight animal cages in a line on the northern perimeter of the zoo. Only four cages were being used: one to hold the gorilla, one for the chimpanzees, one for the gibbons and one for the macaques.

(a) Find the number of ways the four cages can be assigned to the animals so that the cages are next to each other.

It was decided that the gorilla should have at least one empty cage between its cage and the next occupied cage. The other animal cages do not have to be next to each other.

(b) Find the number of ways the four cages can be assigned now.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |

Drag this panel down to reveal the solution

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

©1997 - 2024 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/