Chapter 2.2B, Problem 5A

To determine

(a)

The number of one-to-one correspondences between the sets $\left\{a,b,c,d\right\}$ and $\left\{1,\text{ 2},\text{ 3},\text{ 4}\right\}$, if b must be corresponded to 3.

To determine

(b)

The number of one-to-one correspondences between the sets $\left\{a,b,c,d\right\}$ and $\left\{1,\text{ 2},\text{ 3},\text{ 4}\right\}$, if b must correspond to 3 and d to 4.

To determine

(c)

The number of one-to-one correspondences between the sets $\left\{a,b,c,d\right\}$ and $\left\{1,\text{ 2},\text{ 3},\text{ 4}\right\}$, if a and c must correspond to even numbers.