How is a 2 to 4 decoder related to 4:1 multiplexer?

A 2-to-4 decoder has 2 input (select) lines and 4 output lines; for every combination of the 2 inputs exactly one of the 4 outputs becomes 1 (it generates each of the 4 minterms of the 2 input variables). A 4:1 multiplexer has 4 data-input lines, 2 select lines and a single output; the same 2 select lines choose which one of the 4 data inputs is passed to the output. So a 2-to-4 decoder is essentially the selecting/enabling core of a 4:1 MUX: if each decoder output line is ANDed with the corresponding data input, and the four AND outputs are ORed together, the result is exactly a 4:1 multiplexer - both circuits use the same 2 select lines to distinguish among the same 4 possibilities.