Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

A restaurant has rectangular tables. Each table has space for four people: two seats are placed along each of the table’s longer sides (see diagram). Eight friends have reserved two tables, $X$ and $Y$. Rajid, Sue and Tan are three of these friends.
(a)[3]

The eight friends are to be split into two groups of $4$, with one group assigned to table $X$ and the other to table $Y$. Determine how many different ways this can be done if Rajid and Sue have to be at the same table as each other and Tan has to be at the other table.

(b)[3]

When the friends arrive at the restaurant, Rajid and Sue decide to sit together at table $X$ on the same side. Tan says that he does not care which table he is at. Find the number of different seating arrangements for the $8$ friends.

(c)[4]

When they leave the restaurant, the $8$ friends line up for a photograph. Find the number of different arrangements if Rajid and Sue stand next to each other, but neither one is at an end of the line.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies combinations $^5C_2\times2$ or an equivalent expression.

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