For a given matrix, let \(R_i\) denote the sum of all entries in its \(i^{\text {th }}\) row and \(C_j\) denote the sum of all entries in its \(j^{\text {th }}\) column. How many \(3 \times 3\) matrices with nonnegative integer entries are there such that \(R_1=R_2=C_1=C_2=2\) and \(R_3=C_3=1\) ?

• A

  12
• Correct answer
  B

  11
• C

  14
• D

  13

Hence, the correct answer is option: 'B'.