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.
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?
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
Reiny,
Thank you so very much!!!
You are welcome, sorry about the error.
Good for you to catch it.
To determine the possible digits for the four-digit number, all we need to do is consider the range of digits mentioned, which is from 0 to 7. In this case, the possible digits would be 0, 1, 2, 3, 4, 5, 6, and 7. Hence, we include the digit 0 in the range.
Now, let's break down the question further to determine the solution step by step. We are looking for odd four-digit numbers, where all the digits are different, and the number must contain the digit 4.
Step 1: The first digit options
Since the number cannot start with a leading zero, we have seven options for the first digit (1, 2, 3, 4, 5, 6, 7).
Step 2: The second digit options
We need to select the second digit, excluding the digit we have already used in the first step. In this case, we have six available digits remaining.
Step 3: The third digit options
We need to select the third digit, excluding the two digits already used. Therefore, we have five available digits remaining.
Step 4: The fourth digit options
Here, we need to select the fourth digit, excluding the three digits used previously. We have four available digits remaining.
Step 5: Determine the total number of possibilities
To find the total number of possibilities, we multiply the options from each step together:
7 options (first digit) × 6 options (second digit) × 5 options (third digit) × 4 options (fourth digit) = 840.
Thus, there are 840 odd four-digit numbers, with all the digits different, that can be formed from the digits 0 to 7, considering the condition that the number must contain the digit 4.