Math Help - probability of repeating digit

1. probability of repeating digit

Hi!

What is the probabilty that in a 10-digit number, digit 7 repeats 6 times (no more or less, exactly)?

or in other words, what is the probability that in a random 10-digit number there will be 6 sevens.

thanks

2. Re: probability of repeating digit

Originally Posted by Kiiefers
What is the probabilty that in a 10-digit number, digit 7 repeats 6 times (no more or less, exactly)?
or in other words, what is the probability that in a random 10-digit number there will be 6 sevens.
First by "10-digit number' you must mean the leading digit cannot be 0.
So there are $9\cdot 10^9$ 10-digit numbers.

Of those, there are $\binom{9}{5}\cdot 9^4$ that begin with a seven and have exactly five other sevens.

There are $8\cdot\binom{9}{6}\cdot 9^3$ that do not begin with a seven and have exactly six sevens.

3. Re: probability of repeating digit

Thanks.
What those brackets in this case mean?

Combinations or variations?

4. Re: probability of repeating digit

Originally Posted by Kiiefers
What those brackets in this case mean?
Combinations or variations?

$\binom{N}{k}=\frac{N!}{k!(N-k)!}$