Higher June 2019 Paper 1 Q18
18. Ravi needs to choose a 5-character passcode for a door lock.
He chooses to use 5 of these 7 characters:
1 9 6 7 R P #
Each chosen character is used only once.
(a) Find the number of different 5-character passcodes Ravi can make. [2]
(b) Find the probability that Ravi’s 5-character passcode starts with R and ends with P. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 2520 | B2 | B1 for \(7\times6\times5\times4\times3\) oe |
| Scheme | Marks | Comments |
|---|---|---|
| 60 or \(\dfrac{5\times4\times3}{7\times6\times5\times4\times3}\) or \(\dfrac17\times\dfrac16\) | B2 | B1 for \((1\times)\ 5\times4\times3\ (\times1)\) oe seen |
| \(\dfrac{60}{2520}\) oe; ISW; | B1 | FT \(\dfrac{\text{'their derived 60'}}{\text{'their derived (a)'}}\) NB an answer of \(\dfrac{120}{5040}\) following an answer of 5040 in (a) earns B0 B1FT here, so not from wrong working |
| (5) |