AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

Consider N(A)=m and N(B)=n
PB has 112 elements more than PA
N(PB)‌‌=112+N(PA)
N(PB)−N(PA)‌‌=112
2n−2m‌‌=16×7
Rewrite the above equation.
2m(2n−m−1)=16×7
2m(2n−m−1)=24(23−1)
From the above equation,
m‌‌=4
n−m‌‌=3
n−4‌‌=3
n‌‌=7
The number of injective function from A to B
=N(B)PN(A)
=7P4
=‌

7!

3!

=840