Here it is an example of Binomial Distribution..As there is 7 trials and the population(no of total coupons is 15) is although finite but we are using with replacement..As we know :
In each trial , the probability remains the same..
So P(at most 9) = 9 / 15 = 3 / 5
As 7 times coupon is chosen with replacement ..So
P(at most 9) remains same at each trial..
Hence P(event) = 3/5 * 3/5 *...................7 times
= (3/5)7
Hence D) is the correct answer..