Let $S_1=\left\{\left(i,j,k\right) :i,j,k\in \left\{1,2,\dots ,10\right\}\right\}$

$S_2=\left\{\left(i,j\right) :1\le i<j+2\le 10,i,j\in \left\{1,2,\dots ,10\right\}\right\}$

$S_3=\left\{\left(i,j,k,l\right):1\le i<j<k<l,i,j,k,l\in \left\{1,2,\mathrm{.....},10\right\}\right\}$

and  $S_4=\left\{\left(i,j,k,l\right) : i,j,k \text{and} l \text{are distint elements in} \left\{1,2,...,10\right\}\right\}$

If the total number of elements in the set $S_r$ is $n_r,r=1,2,3,4$ then which of the following statements is (are) TRUE?

• Correct answer
  A

  $n_1=1000$
• Correct answer
  B

  $n_2=44$
• C

  $n_3=220$
• Correct answer
  D

  $\frac{n_4}{12}=420$

Hence, the correct answer is options: 'A', 'B', 'D'.