Can u help me with this combination question.? It is very difficult, higher Year 11 level.

Question

anonymous · Answer

The Gladstone harbour board decides to issue private boats uusing the Gladstone harbour with 7 digit registration numbers. None of these can start with zero. The harbour board had only been able to get the digits 0, 1, 2, 3, 4, 5, 7, 9 for the boat registration numbers. No digit may be used more than once in each registration number.
Bruno, who was responsible for allocating the registration numbers to the boats, had the bright idea of using the number 9 upside down to make 6. However, the 6 and 9 cannot both occur in th same registration number. 
The registration numbers are issued in ascending orider. Thus the first registration number is 1023567. The next two are 1023576 and 1023579.
How many boats can have registration numbers staring with 6?

anonymous · Answer

7!
6 is the 1st number.  then you have 7 #'s left to chose from to putin ith eth next spot, 6, then 5 then 4 and so on.

anonymous · Answer

do u have to take in account that u cant have 6 and 9 in the same number plate

anonymous · Answer

$$\left[\begin{matrix}6 & \alpha & \beta & \gamma & \delta & \epsilon & \eta\ 1st & 2nd & 3rd & 4th & 5th & 6th & 7th\end{matrix}\right]$$

anonymous · Answer

yes, so we exclude 9 altogether because the number starts with 6.

anonymous · Answer

$$\text {there are } 7 \text{ choices for } \alpha \text{, } 6 \text{ choices for }\beta \text{, and so on}$$

anonymous · Answer

so it is 7x6x5x4x3x2

anonymous · Answer

yep

anonymous · Answer

what would the leaf and tree diagram look like