Fifteen coupons are numbered 1, 2, 3,....,15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on the selected coupon is 9 is

 Total ways ${15}^7$
For favorable ways, we must have 7 selected coupons numbered from 1 to 9 so that
‘9’ is selected at least once. Thus total number of favorable ways is,  $9^7-8^7$ 
$\Rightarrow$ Required probability =  $\frac{9^7-8^7}{{15}^7}$