If the only contents of a container are 10 disks that are each numbered with a different positive integer from 1 through 10, inclusive. If 4 disks are to be selected one after the other, with each disk selected at random and without replacement, what is the probability that the range of the numbers on the disks selected is 7?
So I don't understand why my solution doesn't work:
I figured if there are 4 draws, then to pick, say, $1,8$,and two numbers between $1$ and $8$, the probability would be $(1/10)*(1/9)*(6/8)*(5/7)$. You have a $1/10$ chance to pick $1$. Since there's no replacement, you have $1/9$ chance to pick $8$. then $6/8$ for integers $2,3,4,5,6,$ and $7$. Then $5/7$ for another one.
Then just multiply by three. But apparently I don't get anything close to the solution. Could someone please explain why this is?
Update: I finally get it. Thank you all for the responses!