Step 1 :This is a problem of combinations. Each ingredient (ham, mustard, mayo, cheese) can be either included or not included in the sandwich. So for each ingredient, there are 2 possibilities. Since there are 4 ingredients, the total number of combinations would be \(2^4\).
Step 2 :Calculate the total number of combinations: \(num\_ingredients = 4\)
Step 3 :Calculate the total number of combinations: \(num\_combinations = 2^{num\_ingredients} = 16\)
Step 4 :Final Answer: The number of ways you can order a sandwich is \(\boxed{16}\).