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Assertion $(A)$ : If set $A$ contains $7$ elements and set $B$ contains $6$ elements, then the number of one $-$ one onto mapping from $A$ to $B$ is $420$ .
Reason $(R)$ : If $A$ and $B$ are two non $-$ empty sets containing $m$ and $n$ elements respectively, then number of one $-$ one onto functions from $A$ to $B$
$=\left\{n !, \text { if } m=n \ 0, \text { if } m \neq n \right. \text {. \}}$

• A
  Both $(A) $ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
• B
  Both $(A) $ and $(R)$ are true but $(R)$ is not the correct explanation of $(A)$.
• C
  $(A)$ is true but $(R) $ is false.
• ✓
  $(A)$ is false but $(R)$ is true.