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Fifteen coupons are numbered from 1 to 15. Seven coupons are selected at random one at a time with replacement. What is the probability that the largest number appearing on a selected coupon is 9 ?

 

The solution provided is (3/5)^7 but from the language of question I think there must be at least one 9

hence I think the solution should be $\frac{9^{7}-8^{7}}{15^{7}}$
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It says..,largest number appearing on selected coupon is 9...

That means the largest number randomly selected should not exceed 9...or maximum 9

So I think we can choose in (9^7)/(15^7) only......!!!!

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Please correct me if i am wrong ..what i am thinking is cards are numbered from 1 to 15 ..we have tp find the probability when seven cards selected the largest number appearing on a card is 9 so until an unless the other 6 are either of 1,2,3,4,5,6,7,8 this is not possible so i counted like that and there are 7 * 8c6 ways of selecting such type of cards  total ways of selecting 7 cards out of 15 is 15c 7 so probability is (7*8C6)/15c7 ...please check my answer
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