Posted by Ann on .
Regarding my question below, when the question talks about digits 07 do we include the 0. In other words, are the possible digits 0,1,2,3,4,5,6,7 or 1,2,3,4,5,6,7? Thanks again for your help.
How many odd fourdigit numbers, all of the digit different can be formed from the digits 0 to 7, if there must be a 4 in the number?

Math (Reiny) 
Reiny,
Ann, you are right,
I read the question rather superficially and did not fully register that the zero was included, and we had 8 digits instead of 7
I will also assume that a 4digit number would not start with a 0.
so lets look at those 3 cases again.
case 1: starts with a 4 and ends with an odd, placing the odd digits in 4 ways in the 4th place.
1x6x5x4 = 120
case 1: the "4" is in the second position, but that means we cannot start with a 0
5x1x5x4 = 100 , the zero could go in the 3rd place
case 3: same as case 2 , 5x5x1x4
= 100
total = 120+100+100 = 320
This is is reference to question
http://www.jiskha.com/display.cgi?id=1294266559 
Math (Reiny) 
Ann,
Reiny,
Thank you so very much!!! 
Math (Reiny) 
Reiny,
You are welcome, sorry about the error.
Good for you to catch it.