Seven coupons are selected at random one at a time with replacement from 15 coup

Question

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

Options:

A . (916)6

B . (815)7

C . (35)7

D . (35)7 - (815)7

Answer: Option D
:
D
Each coupon can be selected in 15 ways. The total number of ways of choosing 7 copouns is

15^{7}

. If largest number is 9, then the selected numbers have to be from 1 to 9 excluding those consisting of only 1 to 8.
Probability desired is

\frac{9^{7} - 8^{7}}{15^{7}}

= {(\frac{3}{5})}^{7} - {(\frac{8}{15})}^{7}

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