A and B are two sets such that n(A) = 5 and n(B) = 7 . The number of…

The correct answer is Option (3) → 2520

In a one-one function, different elements of A have different images in B. The 5 elements of A can be given images one by one:

    first element: 7 choices, second: 6, third: 5, fourth: 4, fifth: 3

So the number of one-one functions is

    \(\displaystyle ^{7}P_{5} = \frac{7!}{2!} = 7 \times 6 \times 5 \times 4 \times 3 = 2520\)