What is the digit at the unit place of the sum (0!) + (1!) + (2!) + (3!) + (4!) where ! denotes factorial?

Explanation:

Step 1: Calculate individual factorials

• 0!: By definition, the factorial of 0 is 1. Therefore, 0! = 1.
• 1!: The factorial of 1 is also 1. Therefore, 1! = 1.
• 2!: The factorial of 2 is calculated as 2 × 1 = 2. Therefore, 2! = 2.
• 3!: The factorial of 3 is calculated as 3 × 2 × 1 = 6. Therefore, 3! = 6.
• 4!: The factorial of 4 is calculated as 4 × 3 × 2 × 1 = 24. Therefore, 4! = 24.

Step 2: Write down the unit digits of the factorials

• The unit digit of 0! is 1.
• The unit digit of 1! is 1.
• The unit digit of 2! is 2.
• The unit digit of 3! is 6.
• The unit digit of 4! is 4 (since 24 ends in 4).

Step 3: Add the unit digits

Now, we add the unit digits of the factorials to find the unit digit of their sum:

1 (from 0!) + 1 (from 1!) + 2 (from 2!) + 6 (from 3!) + 4 (from 4!) = 14.

The unit digit of 14 is 4.

Step 4: Conclusion

The digit at the unit place of the sum (0!) + (1!) + (2!) + (3!) + (4!) is 4.

Correct Answer: Option 3) 4