# Ten tickets numbered 1, 2, 3, ..., 10. Six tickets are selected at random one of a time with replacement.

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Ten tickets numbered $1, 2, 3, \ldots 10.$ Six tickets are selected at random one at a time with replacement.  The probability of the largest number appearing on the selected ticket being $7$ is ________

1. $(7^6 +1)/10^6$
2. $(7^6 - 6^6)/10^6$
3. $(7^6+6^6)/10^6$
4. $6^6/10^6$

$\#$ways to select $6$ tickets when the highest number is between $1$ to $7$ with replacement = $7^6$

$\#$ways to select $6$ tickets when the highest number is between $1$ to $6$ with replacement = $6^6$

Now $7^6 – 6^6$ will give all the possibilities when highest number is $7$

$\#$ways to select $6$ tickets out of $10$ with replacement = $10^6$

$\therefore \text{Required probability} = \large\frac{7^6 – 6^6}{10^6}$

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