# Exam-Style Question on Combinatorics

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 695. This question is similar to one that appeared on an IB AA Higher paper in 2021. The use of a calculator is allowed.

Nine cats squeeze through a gap in a fence to get to a fish pond. There is only enough room for one cat at a time to squeeze through the gap.

Seefer and Sushi are two of the nine cats attracted to the fish pond.

Find the total number of possible ways in which the nine cats can squeeze through the gap if Seefer passes through

(a) in the position immediately after Sushi;

(b) in any position after Sushi.

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