Given n(A)=5 and n(B)=7.
A one-one function assigns each element in set A to a different element in set B. No two elements from A can map to the same element in B.
For the 1st element of A: 7 choices from B
For the 2nd element of A: 6 remaining choices
For the 3rd element of A: 5 remaining choices
For the 4th element of A: 4 remaining choices
For the 5th element of A: 3 remaining choices
Total number of one-one functions:
7×6×5×4×3
=42×5
=210×4
=840×3
=2520
This can also be calculated using the permutation formula:
nPr=(n−r)!n!
Where n=7 and r=5:
7P5=(7−5)!7!
=2!7!
=2520
Therefore, the number of one-one functions from A to B is 2520.