Permutations & Combinations
Digit parity counting
nta_pyq_2025_apr
Grade 12
Question:
If the number of$seven-digit$numbers, such that the sum of their digits is even, is m$\cdot n$$\cdot 10$; n m, n$\i_n {1, 2, 3,$$\ldots, 9}, then$m + n$is equal to _______$
Step-by-Step Solution
Key Concept: Count$seven-digit$numbers by parity of digit sum using$even/odd$digit choices and nonzero leading digit.
Total 7 digit nos. = 9000000$(14)$7 digit nos. having sum of digits$Even = 4500000$$5 = 9.5$$\cdot 10$m = 9$,$n = 5$$$$m + n = 1$4$
Correct Answer: 14