Number of Functions Possible from Set A to Set B

Q. Let $A=\{1,2,3,4,5,6\}$ and $B=\{a,b,c,d\}$, then the total number of possible functions from $A$ to $B$

1. without any restriction is $6^4$
2. such that every element in $B$ has atleast one pre-image is $1560$
3. such that all the elements in $B$ should not have pre-image is $2536$
4. without any restriction is $4^6$

Q. Number of functions from a set $A$ containing $6$ elements to a set $B$ containing $3$ elements such that every element in $B$ has atleast one preimage is

1. $3^6-{}^3{C}_1-{}^3{C}_2(2^6+2)$
2. $3^6-{}^3{C}_1-{}^3{C}_2\left(2^6\right)$
3. $534$
4. $540$

Q. The number of bijections of a set consisting of 10 elements to itself is :

1. $\angle 10$
2. $\angle 10-10$
3. $\angle 9+10$
4. $\angle 10-2$