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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.. 

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