A function is defined as  $f:\{a_1,a_2,a_3,a_4,a_5,a_6\}\to \{b_1,b_2,b_3\}$ . Now, match the following lists:

	List -I		List -II
a)	Number of surjective functions	p)	540
b)	Number of functions in which  $f\left(a_i\right)\ne b_i$	q)	0
c)	Number of invertible functions	r)	216
d)	Number of many one functions	s)	729

a) Number of surjective functions is 
 $3^6-{}^{3}C_1{(3-1)}^6+{}^{3}C_2{(3-2)}^6=729-192+3=540$
b) If  $f\left(a_1\right)\ne b_i$ , then pre-image  $a_1,a_2,a_3$  cannot be assigned images $b_1,b_2,b_3$ ,  respectively.
Hence, each of  $a_1,a_2,a_3$  can be assigned images in 2 ways. 
$a_4,a_5,a_6$  can be assigned images in 3 ways each. Hence number of functions is  
c) One-One functions are not possible as pre-images are more than images.
d) Number of many-one-functions is $2^3{3}^3=216.$
Total number of functions – Number of one-one functions 
= $3^6-0=729$  .