Instructions
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Question
Amy, Ali, the Tan family (consisting of $1$ members) and $2$ other people are together one day.
They line up for a photograph in a straight line. Find the number of ways they can be arranged such that
- Ali and Amy are next to each other,
- the Tan family are not all next to one another,
- members of the Tan family are separated by at least 1 other person,
- either Ali and Amy are next to each other, or the Tan family are all next to one another, or both.
They now visit a restuarant and is seated at a round table. Find the number of ways they can be arranged such that
- there are $3$ seats and there are no restrictions,
- there are $4$ seats and the Tan family are all next to one another,
- there are $5$ seats and there are no restrictions.
Answer
- $6$
- $7$
- $8$
- $9$
- $10$
- $11$
- $12$
$13$