Question

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

• A. ${\left(\frac{9}{10}\right)}^6$
• B. ${\left(\frac{8}{15}\right)}^7$
• C. ${\left(\frac{3}{5}\right)}^7$
• D. $noneofthese$

Answer 1

The correct option is D $noneofthese$

Since, there are $15$ possible cases for selecting a coupon and seven coupons are selected, the total number of cases of selecting seven coupons $={15}^7$
It is given that the maximum number on the selected coupon is $9$, therefore the selection is to be made from the coupons numbered $1$ to $9$.
This can be made in $9^7$ ways. Out of these $9^7$ cases,$8^7$ does not contain the number $9$. Thus, the favourable number of cases $9^7-8^7$.
Hence, the required probability $=\frac{9^7-8^7}{{15}^7}$