Answer:
Option B
Explanation:
Given , X has exactly 5 elements and Y has exactly 7 elements.
n(X) =5
n(Y) =7
Now ,number of one-one functions from X to Y is
$\alpha = ^{7}P_{5} =^{7}C_{5}\times 5!$
Number of onto functions from Y to X is β
1,1,1,1,3 or 1,1,1,2,2
$\beta =\frac{7!}{3!4!}\times 5! +\frac{7!}{(2!)^{3}3!}\times 5!$
= $(^{7}C_{3}+3^{7}C_{3})5!=4\times ^{7}C_{3}\times 5!$
$\frac{\beta -\alpha}{5!}=\frac{(4\times ^{7}C_{3}-^{7}C_{5})5!}{5!}$
= $4\times 35-21=140-21=119$
