# Thread: Combination and Permutation question

1. ## Combination and Permutation question

Hi guys, I'm new to the field of probability and statistics, I have a question that I can't seem to be able to solve, it would be a great help if you guys can help me out understand it.

Question: For a 7 digit phone number, you have already known the first 3 digits. Given that only 2 digits out of the remaining unknown digits are repeated, what is the probability of reaching the right person assuming one person has only one phone number?

My assumption and progress.. Considering i'm still new to the field, i have only managed to get as far as for 4 numbers, the probability of getting the right combination must be 1/10,000 since there are 10,000 different combinations for 4 numbers. But when the question stated that there are repetitive digits I got kinda lost, any help with a detailed solution would be really appreciated.

2. ## Re: Combination and Permutation question

This was my best attempt at it..

considering the number is 015-xxyy

X can be any number from 0-9, which means 10 possible numbers
and since there are 2x, then its 10 x 10 = 100.
the the Y is the repetitive number, and it can be from 0-9, which means also 10 possible numbers.
The y can be arranged in 6 different forms=yyxx xyyx xxyy yxyx xyxy yxxy
that means 10*6=60
next step should be multiplying the X with the y, 100*60=6000 so it should be 1/6000 chance to get the number correctly.

3. ## Re: Combination and Permutation question

The last part of the question is worded poorly. I think the repetitive part may be just a trick or extra fluff!

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