There are 5 distinct ice cream flavors, 5 distinct cones, and 5 distinct toppings. I gather all 15 distinct supplies. There are 5 people. Each person has to get a cone, flavor, and topping, and I can give them any combination of cone, flavor, topping that I want. I don't have to complete one ice cream at a time. For example, I can give everyone a cone, and then the flavor, and then the topping.
However, I have to give a cone first before I give the ice cream, and I have to give ice cream before I give a topping.
How many ways can I hand out supplies under these constraints? (I can only do one action at a time).
My thoughts: I have to give a cone first, and there are 5 distinct cones, so 5 choose 1. Then, I can give a cone, or the flavor as the second step, so another 5 options. But I'm stuck on what to do from here.