Quandaries
and Queries 

hi i am behzad and from iran i am a teacher i saw the question below in the internet but i didn't manage to get the exact answer that was in the site i think the level of the question is secondary(?) How many sixdigit numbers contain at least one 7 in their decimal expansion? i'll be much more thankful if you intruduce sites with questions and answers about probability thanks a lot BEHZAD 

Hi Behzad, If you are going to form a six digit number from the ten digits 0,1,2,3,4,5,6,7,8,9 then the first digit can't be 0, so you have 9 choices for the first digit. Each of the remaining digits can be any of the 10 digits and hence there are
Rather than count the number of such six digit numbers that contain at least one 7 I am going to count the number that have no 7's. Hence I want to count the six digit numbers that can be formed from the digits 0,1,2,3,4,5,6,8,9. As before the first digit can't be 0 so there are 8 choices for the first digit. Each of the remaining digits can be any of the 9 digits and hence there are
The remaining six digit numbers contain at least one 7 and hence the number of six digit numbers that contain at least one 7 is
Penny 

