The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3,4,5 and 6 without repetition is

Options

A. 432
B. 108
C. 36
D. 18

Answer

To find the sum of the digits in the unit's place of all the 4-digit numbers formed by using the digits 3, 4, 5, and 6 without repetition, we can follow these steps:

### Step 1: Identify the digits and the total number of 4-digit combinations
We have the digits 3, 4, 5, and 6. Since we are forming 4-digit numbers using these 4 digits without repetition, we can use all of them.

### Step 2: Determine the unit's place contribution of each digit
Each digit (3, 4, 5, 6) will appear in the unit's place of the 4-digit numbers. To find out how many times each digit appears in the unit's place, we can calculate the number of arrangements of the other three digits.

### Step 3: Calculate the number of arrangements for the other digits
The number of ways to arrange the remaining three digits (after fixing one digit in the unit's place) is given by \(3!\) (3 factorial), which equals 6.

### Step 4: Calculate the contribution of each digit in the unit's place
- If 3 is in the unit's place, the contribution is \(3 \times 6 = 18\).
- If 4 is in the unit's place, the contribution is \(4 \times 6 = 24\).
- If 5 is in the unit's place, the contribution is \(5 \times 6 = 30\).
- If 6 is in the unit's place, the contribution is \(6 \times 6 = 36\).

### Step 5: Sum the contributions
Now, we can sum the contributions from all digits:
\[ 18 + 24 + 30 + 36 = 108 \]

### Final Answer
The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3, 4, 5, and 6 without repetition is **108**.

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