there is a machine with $8$ toys in it that each cost between $25$ cents and $2$ dollars, with each toy being $25$ cents more expensive than the next most expensive one. each time sam presses the big red button on the machine, the machine randomly selects one of the remaining toys and gives sam the option to buy it. if sam has enough money, he will buy the toy, the red button will light up again, and he can repeat the process. if sam has $8$ quarters and a ten dollar bill and the machine only accepts quarters, what is the probability that sam has to get change for the $10$ dollar bill before he can buy his favorite toy- the one that costs $\$1.75$? express your answer as a common fraction.