Regarding my question below, when the question talks about digits 0-7 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.

Question

How many odd four-digit numbers, all of the digit different can be formed from the digits 0 to 7, if there must be a 4 in the number?

Answer 1

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 4-digit 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

Answer 2

Reiny,

Thank you so very much!!!

Answer 3

You are welcome, sorry about the error.
Good for you to catch it.