The number of distinct quadratic equations $a x^2+b x+c=0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c(a \neq b \neq c)$ from the set $\{0,1,2,4\}$ is

• A

  $4$
• Correct answer
  B

  $6$
• C

  $5$
• D

  $12$

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