Let $$\begin{gathered}
S _ { 1 } = \{ ( i , j , k ) : i , j , k \in \{ 1,2 , \ldots , 10 \} \} , \\
S _ { 2 } = \{ ( i , j ) : 1 \leq i < j + 2 \leq 10 , i , j \in \{ 1,2 , \ldots , 10 \} \} , \\
S _ { 3 } = \{ ( i , j , k , l ) : 1 \leq i < j < k < l , \quad i , j , k , l \in \{ 1,2 , \ldots , 10 \} \}
\end{gathered}$$ and $$S _ { 4 } = \{ ( i , j , k , l ) : i , j , k \text { and } l \text { are distinct elements in } \{ 1,2 , \ldots , 10 \} \} .$$ 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 ? (A) $n _ { 1 } = 1000$ (B) $n _ { 2 } = 44$ (C) $n _ { 3 } = 220$ (D) $\frac { n _ { 4 } } { 12 } = 420$
Let
$$\begin{gathered}
S _ { 1 } = \{ ( i , j , k ) : i , j , k \in \{ 1,2 , \ldots , 10 \} \} , \\
S _ { 2 } = \{ ( i , j ) : 1 \leq i < j + 2 \leq 10 , i , j \in \{ 1,2 , \ldots , 10 \} \} , \\
S _ { 3 } = \{ ( i , j , k , l ) : 1 \leq i < j < k < l , \quad i , j , k , l \in \{ 1,2 , \ldots , 10 \} \}
\end{gathered}$$
and
$$S _ { 4 } = \{ ( i , j , k , l ) : i , j , k \text { and } l \text { are distinct elements in } \{ 1,2 , \ldots , 10 \} \} .$$
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 ?\\
(A) $n _ { 1 } = 1000$\\
(B) $n _ { 2 } = 44$\\
(C) $n _ { 3 } = 220$\\
(D) $\frac { n _ { 4 } } { 12 } = 420$