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AP EAMCET · Maths · Permutation Combination

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is

  1. A \(18 \times 7!\)
  2. B \(24 \times 7!\)
  3. C \(36 \times 7!\)
  4. D \(72 \times 7!\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(36 \times 7!\)

Step-by-step Solution

Detailed explanation

Sum of 10 digits \(S_{10} = 0+1+...+9 = 45\). For an 8-digit number to be divisible by 9, the sum of its 8 digits \(S_8\) must be divisible by 9. Let \(d_1, d_2\) be the two excluded digits. \(S_8 = 45 - (d_1+d_2)\). For \(S_8\) to be divisible by 9, \(d_1+d_2\) must be…