Question 9
In a lottery game, a player chooses $6$ distinct positive integers from $1$ to $42$.
A sample of the lottery ticket is shown below:
Now, Alex considers a ticket perfect if all the digits from $1$ to $9$ are used exactly once in the selected numbers, and the digit $0$ is not used at all. For example, he can select $7,8,9,14,25$ and $36$, as shown in the diagram below:
In how many ways can he fill out a perfect ticket?
A sample of the lottery ticket is shown below:
Now, Alex considers a ticket perfect if all the digits from $1$ to $9$ are used exactly once in the selected numbers, and the digit $0$ is not used at all. For example, he can select $7,8,9,14,25$ and $36$, as shown in the diagram below:
In how many ways can he fill out a perfect ticket?