Determine how many one-to-one correspondences are possible between two sets...

Question

Determine how many one-to-one correspondences are possible between two sets, {n,t,z,w,v} and {1,2,3,4,5}, given the following conditions.

 

a. If in each correspondence n must match with 2.

b. If in each correspondence n must match with 2 and t must match with 1.

c. If in each correspondence n, t, z must match with an odd number.

 

Help please. How do I solve this type of problem? Any help is appreciated. Thank you. 

Answer 1

a)   4! = 24

     There are 4 choices for t, 3 for z, 2 for w, one for v

 

b)  3! = 6

     there are 3 choices for z, 2 for w, and one for v

 

c)   3*2*2= 12

     there are 3 choices for n, 2 for t, one for z, two (choices of even) of w and 1 for v.