Determine how many​ one-to-one correspondences are possible between two​ sets, {p, y, z, w, v} and​ {1, 2,​ 3, 4,​ 5}, given the following conditions. Please help ):

Question

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

a. If in each correspondence pp must match with 33.

b. If in each correspondence pp must match with 33 and yy must match with 44.

c. If in each correspondence pp​, yy​, and z must match with an odd number.

Answer 1

So then 1,2 and 5 are available

since z must map to an odd #, there are 2 possibilities.

w can map to either 2 or the other odd that is not mapped to z.

Therefore there are 4 possible mappings

z-->1 , w -->2, v-->5

z-->1 w-->5, v--->2

z-->5, w--->2, v-->1

z--->5, w--->1, v--->2