jmc

There are five slots on which the spinner can land with each spin; thus, there are 125 total possibilities with three spins. The only way in which you can earn exactly \ 1700$inthreespinsisbylandingona$ \$300$, a \ 400$,anda$ \$1000$. You could land on any one of the three in your first spin, any one of the remaining two in your second spin, and the remaining one in your last spin, so there are $3\cdot 2\cdot 1=6$ ways in which you can earn \ 1700$.Thus,theprobabilityis$\boxed{\frac{6}{125}}$.