Paragraph: Box $1$ contains three cards bearing numbers $1,2,3$; box $2$ contains five cards bearing numbers $1,2,3,4,5$; and box $3$ contains seven cards bearing numbers $1,2,3,4,5,6,7$. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the $i^{t h}$ box, $i=1,2,3$.
Question: The probability that $x_{1}+x_{2}+x_{3}$ is odd, is

• A

  $\frac{29}{105}$
• Correct answer
  B

  $\frac{53}{105}$
• C

  $\frac{57}{105}$
• D

  $\frac{1}{2}$

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