If all the six digit numbers x₁x₂x₃x₄x₅x₆ with 0 < x₁ < x₂ < x₃ < x₄ < x₅ < x₆ are arranged in the increasing order, then the sum of the digits in the 72nd number is _____.
Step-by-Step Solution
Key Concept: Six strictly increasing digits chosen from 1–9. Count how many numbers start with each prefix to locate the 72nd.
Numbers starting with 1,2: ⁷C₄=35; with 1,3: ⁶C₄=15; with 1,4: ⁵C₄=5; with 1,5: ⁴C₄=1; with 2,3: ⁶C₄=15. Total up to 2,3,...=71. The 72nd number is 2,4,5,6,7,8. Sum = 2+4+5+6+7+8 = 32.
Correct Answer: 32