I have a list of survey responses that include different job titles. I want to search and count how many people put down a military related profession. I tried using the following code but it didn't work.

=COUNTIF($A$2:$A$350,OR("*" & "military" & "*","*" & "army" & "*","*" & "air force" & "*", "*" & "marines" & "*", "*" & "navy" & "*"))

The responses include multiple jobs in each cell which is why I am trying to see if the text I'm searching for is contained in the cell.

Can I do this in one formula or am I going to have to do a countif for each term and aggregate it?