Incorrect spelling, explanation: programms is probably a mistake made by mixing up two different spellings: American programs and British programmes. The American programs (singular program) is a form simplified from the British in Webster’s dictionary in the 19th century. Therefore programms is incorrect, and the correct form is programs (or programmes).

Correct spelling, explanation: the correct spelling of this word is programs in American English or programmes in British English. The British version (singular programme) comes from Latin programma. The American spelling, programs (singular program) was simplified in Webster’s dictionary, as many other words with confusing spellings. Programms is an unnecessary mixture of the two different spellings and is incorrect.

Definition of programs:
noun, plural of program, a summary of the order of events, a schedule of an event
They printed too few programs and there were not enough for everybody.
– Have you seen the wedding programs? They are cute! – They are, but I think it’s a pointless waste of money.