Question

How many one-to-one functions are there from a set with two elements to a set with four elements?

Answer 1

12

Explanation:

There are 4×3 = 12 ways that two of the four elements can be mapped to the two elements of the smaller set. Here's a list of the 12 possible functions:

{(a, 1), (b, 2}}, {(a, 2), (b, 1)}, {(a, 1), (b, 3)}, {(a, 3), (b, 1)},

{(a, 1), (b, 4)}, {(a, 4), (b, 1)}, {(a, 2), (b, 3)}, {(a, 3), (b, 2)},

{(a, 2), (b, 4)}, {(a, 4}, (b, 2)}, {(a, 3), (b, 4)}, {(a, 4), (b, 3)}