# Math Help - 6 digit number

1. ## 6 digit number

we want to create a 6 digits number from the digits 1-5, and to keep the condition that each of the 5 digits, appear at least once. what is the probability that the number 11 ( the digit 1 twice ), will appear ? ( meaning what is the prob that 1 will appear twice and in a row )

cheers

2. Originally Posted by WeeG
we want to create a 6 digits number from the digits 1-5, and to keep the condition that each of the 5 digits, appear at least once. what is the probability that the number 11 ( the digit 1 twice in a row )?
In each of those 6-digit numbers there will be five different digits and one which repeats.
There are 5 ways to pick the one that repeats.
Then there are $\frac{6!}{2}$ ways to arrange these six digits.

There are $5!$ ways arrange the string “112345” so that the 1’s are together.