write all the possible odd 5-digit numbers using the digits 1,4,7,8 and 0, with the 1 in the ten thousands places.
1xxx1 or 1xxx7
now just fill in the other 3 digits in the 6 ways possible
To create all possible odd 5-digit numbers using the digits 1, 4, 7, 8, and 0, with the 1 in the ten thousands place, we need to consider the remaining four digits in the remaining four places.
Step 1: Place the fixed digit 1 in the ten thousands place.
Step 2: The remaining four places can have any of the four remaining digits (4, 7, 8, and 0).
Step 3: Since we want to create odd numbers, the units digit (ones place) must be odd. So, it can only be 1 or 7.
Step 4: We need to generate all the possible combinations of the remaining four digits (4, 7, 8, and 0) and the possible odd unit digits (1 and 7).
List of all possible odd 5-digit numbers using the digits 1, 4, 7, 8, and 0, with the 1 in the ten thousands place:
1) 1 0 0 0 1
2) 1 0 0 0 7
3) 1 0 0 4 1
4) 1 0 0 4 7
5) 1 0 0 7 1
6) 1 0 0 7 7
7) 1 0 4 0 1
8) 1 0 4 0 7
9) 1 0 4 4 1
10) 1 0 4 4 7
11) 1 0 4 7 1
12) 1 0 4 7 7
13) 1 0 7 0 1
14) 1 0 7 0 7
15) 1 0 7 4 1
16) 1 0 7 4 7
17) 1 0 7 7 1
18) 1 0 7 7 7
19) 1 4 0 0 1
20) 1 4 0 0 7
21) 1 4 0 4 1
22) 1 4 0 4 7
23) 1 4 0 7 1
24) 1 4 0 7 7
25) 1 4 4 0 1
26) 1 4 4 0 7
27) 1 4 4 4 1
28) 1 4 4 4 7
29) 1 4 4 7 1
30) 1 4 4 7 7
31) 1 4 7 0 1
32) 1 4 7 0 7
33) 1 4 7 4 1
34) 1 4 7 4 7
35) 1 4 7 7 1
36) 1 4 7 7 7
37) 1 8 0 0 1
38) 1 8 0 0 7
39) 1 8 0 4 1
40) 1 8 0 4 7
41) 1 8 0 7 1
42) 1 8 0 7 7
43) 1 8 4 0 1
44) 1 8 4 0 7
45) 1 8 4 4 1
46) 1 8 4 4 7
47) 1 8 4 7 1
48) 1 8 4 7 7
49) 1 8 7 0 1
50) 1 8 7 0 7
51) 1 8 7 4 1
52) 1 8 7 4 7
53) 1 8 7 7 1
54) 1 8 7 7 7
There are 54 odd 5-digit numbers using the digits 1, 4, 7, 8, and 0, with the 1 in the ten thousands place.
To find all possible odd 5-digit numbers using the digits 1, 4, 7, 8, and 0, with the 1 in the ten thousands place, we can follow these steps:
Step 1: Determine the number of choices for each digit place.
Since the first digit (ten thousands place) must be 1, there is only one choice.
For the remaining four digits (thousands, hundreds, tens, and units places), we have five options to choose from: 0, 4, 7, 8, and 1 (which can be used only once).
Step 2: Determine the number of possibilities.
For the thousands, hundreds, tens, and units places, we can have any of the remaining four digits (0, 4, 7, 8) in any order.
Thus, the number of possibilities is calculated by multiplying the number of choices for each place: 4 choices × 4 choices × 4 choices × 4 choices = 256 possibilities.
Step 3: Determine the odd numbers.
From the 256 possibilities, we need to identify the odd numbers. An odd number is any number that leaves a remainder of 1 when divided by 2.
In this case, the last digit (units place) cannot be zero, as it would result in an even number. Therefore, our options for the units place are 1, 7, and 1 (again).
Since the thousands, hundreds, and tens places can be any of the four remaining digits (0, 4, 7, 8) and any digit can be repeated, we have a total of 4 × 4 × 4 = 64 possibilities.
Step 4: Combine the possibilities.
The total number of possible odd 5-digit numbers with the digit 1 in the ten thousands place is given by multiplying the number of possibilities from Step 1 and Step 3:
1 possibility (for the ten thousands place) × 64 possibilities (from Step 3) = 64 possible odd 5-digit numbers.
So, there are 64 possible odd 5-digit numbers using the digits 1, 4, 7, 8, and 0, with the 1 in the ten thousands place.