Higher June 2022 Paper 2 Q21
21. There are 8 seats in the front row of a theatre.
8 friends sit down in this row.
(a) When each friend can sit in any of the 8 seats, find the number of different seating arrangements possible. [2]
(b)
Liesa and Todd are 2 of the 8 friends.
Find the probability that Liesa is sitting in the first seat on the left and Todd is sitting next to her. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 40320 | B2 | B1 for \(8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2\ (\times 1)\) or \(8!\) |
| Scheme | Marks | Comments |
|---|---|---|
| 720 or \(\dfrac18 \times \dfrac17\) | B2 | B1 for \((1 \times 1 \times)\ 6 \times 5 \times 4 \times 3 \times 2\ (\times 1)\) or \(6!\) B1 for sight of \(\frac18\) and \(\frac17\) oe only |
| \(\dfrac{720}{40320}\) or \(\dfrac{1}{56}\) oe | B1 | ISW FT ‘\(\dfrac{\text{their derived } 720}{\text{their derived } 40320}\)’ providing at least B1 previously awarded in both (a) and (b). |
| (5) |