Q71 / 180 · KCET 2021 · Mathematics

$A$ 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

  • A
    28
  • B
    35
  • C
    42
  • Correct answer
    D
    21

Solution

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 $n(B)=5$ ${ }^{n(A)} C_{n(B)}={ }^{7} C_{5}={ }^{7} C_{2}=21$

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

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