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$A$ and $B$ are non-singleton sets and $n(A \times B)=35$. If $B \subset A$, then ${ }^{n(A)} C_{n(B)}$ is equal to
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21
Given, $n(A \times B)=35, B \subset A$
$n(A \times B)=35$
$n(A \times B)=7 \times 5$
$n(A \times B)=n(A) \times n(B)$
$\therefore \quad n(A)=7$ and $n(B)=5$
${ }^{n(A)} C_{n(B)}={ }^{7} C_{5}={ }^{7} C_{2}=21$
$n(A \times B)=35$
$n(A \times B)=7 \times 5$
$n(A \times B)=n(A) \times n(B)$
$\therefore \quad n(A)=7$ and $n(B)=5$
${ }^{n(A)} C_{n(B)}={ }^{7} C_{5}={ }^{7} C_{2}=21$
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