Hi, I'm Ashik. Welcome to JustAnswer. I'm reviewing your question now, and will post back with your reply ASAP
It should have random option. Which model of iPod is this ? Is it iPod Nano 7th Gen ?
identify iPod from here and let me know --> https://support.apple.com/en-in/HT204217
If this is iPod Nano 7th Gen, then it is possible that the repeat function of your iPad nano has turned on and that is preventing the shuffle or random function. You need to change it back or turn it off. Play a song and this will bring the Now Playing screen. Tap the album art once to bring controls if they aren't appearing on screen. Look for the repeat symbol and touch it to turn off or change the Repeat function (You can swipe left or right between screens to display or hide the Repeat and Shuffle options). The repeat symbol looks like two arrows in a loop. Make sure there is no 1 on that arrow symbol. Also, turn on Shuffle function there.
Please let me know if that didn't work, so I will continue to help you.