Question

The digits of the number 235 are permutated to form 6 numbers (including 235). What is the sum of the resulting 6 numbers?

• A. 2320
• B. 2120
• C. 2220
• D. 2310

Hint:

In digit permutation sums, each digit repeats $(n-1)!$ times in each place.

Answer 1

The Correct Option is C

Concept: For 3-digit permutations, each digit appears equally in hundreds, tens, and units places. Explanation: Digits = 2, 3, 5 Sum of digits: \[ 2 + 3 + 5 = 10 \] Each digit appears: \[ (3-1)! = 2 \text{ times in each place} \] Total sum: \[ 2 \times (100 + 10 + 1) \times 10 \] \[ = 2 \times 111 \times 10 = 2220 \]