i need some help on how to make 16 leds blink randomly using CD74HC4067 multiplexer
How far have you got so far, and which part is causing you problems?
Yes, post your code & schematic so far.
That part is not really intended to be sinking or sourcing 20mA with LEDs.
You would have better results electrically by creating your random pattern as an INT and then shifting it out as 2 bytes to two TPIC6B595, which are designed for sinking high currents from LEDs: anodes to +5, cathodes to current limit resistors to shift register outputs.
Benefit - you can also have more than 1 LED on at a time if desired.