Find the sum of unit digits of all different numbers formed from digits 4, 6, 7 and 9.

Answer

To find the sum of the unit digits of all different numbers formed from the digits 4, 6, 7, and 9, we can follow these steps:

### Step 1: Determine the total number of different numbers that can be formed.
Since we have 4 distinct digits (4, 6, 7, 9), we can form numbers using all 4 digits. The total number of different 4-digit numbers that can be formed is given by the formula for permutations of n distinct objects, which is n! (n factorial).

\[ \text{Total numbers} = 4! = 4 \times 3 \times 2 \times 1 = 24 \]

### Step 2: Find how many times each digit appears in the unit place.
In a 4-digit number, each of the 4 digits will appear in the unit place an equal number of times. Since there are 24 total numbers and 4 digits, we can find how many times each digit appears in the unit place by dividing the total numbers by the number of digits.

\[ \text{Times each digit appears in unit place} = \frac{24}{4} = 6 \]

### Step 3: Calculate the sum of the unit digits.
Now we can calculate the contribution of each digit to the unit place. Each digit appears 6 times in the unit place, so we multiply each digit by 6 and then sum them up.

\[ \text{Sum of unit digits} = 6 \times (4 + 6 + 7 + 9) \]

Calculating the sum inside the parentheses:

\[ 4 + 6 + 7 + 9 = 26 \]

Now multiplying by 6:

\[ \text{Sum of unit digits} = 6 \times 26 = 156 \]

### Final Answer:
The sum of the unit digits of all different numbers formed from the digits 4, 6, 7, and 9 is **156**.

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