The number of numbers of four different digits that can be formed from...
The units place can be filled in 2 ways.
The tens place can be filled in 3 ways.
The remaining two places can be filled by any two of the remaining three digits. So, the required number of numbers = 2 * 3 x
3P
2.
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The number of numbers of four different digits that can be formed from...
The units place can be filled in 2 ways.
The tens place can be filled in 3 ways.
The remaining two places can be filled by any two of the remaining three digits. So, the required number of numbers = 2 * 3 x
3P
2.
The number of numbers of four different digits that can be formed from...
To find the number of numbers of four different digits that can be formed from the digits of the number 12 356, such that the numbers are divisible by 4, we can follow the steps below:
Step 1: Understanding the Divisibility Rule
A number is divisible by 4 if the last two digits of the number form a multiple of 4. Therefore, in our case, we need to find four-digit numbers using the digits 1, 2, 3, 5, and 6, where the last two digits form a multiple of 4.
Step 2: Analyzing the Possibilities for the Last Two Digits
To form a multiple of 4, the last two digits of the number can be one of the following combinations:
- 12 (divisible by 4)
- 16 (divisible by 4)
- 32 (divisible by 4)
- 36 (divisible by 4)
- 52 (not divisible by 4)
- 56 (divisible by 4)
- 62 (not divisible by 4)
- 63 (not divisible by 4)
Step 3: Counting the Possibilities
We can see that there are four possible combinations where the last two digits form a multiple of 4: 12, 16, 32, and 36.
For each of these combinations, we need to find the number of ways to choose two different digits from the remaining three digits (1, 3, and 5) to form the first two digits of the four-digit number.
- For the combination 12, we have three choices for the first digit (3, 5, or 6) and two choices for the second digit (3 or 5). So, we have 3 * 2 = 6 possibilities.
- For the combination 16, we have three choices for the first digit (3, 5, or 6) and two choices for the second digit (2 or 3). So, we have 3 * 2 = 6 possibilities.
- For the combination 32, we have three choices for the first digit (1, 5, or 6) and two choices for the second digit (1 or 5). So, we have 3 * 2 = 6 possibilities.
- For the combination 36, we have three choices for the first digit (1, 5, or 6) and two choices for the second digit (2 or 5). So, we have 3 * 2 = 6 possibilities.
Step 4: Calculating the Total Number of Possibilities
To find the total number of possibilities, we sum up the possibilities for each combination:
6 + 6 + 6 + 6 = 24
Therefore, the correct answer is option 'D' - 24.