Math about Christmas Meals

Level pending

One day, a particular family went to a restaurant to have their Christmas dinner. This family has \(4\) children, Adam, Ben, Carrie and David who are choosy over their food. Luckily, the restaurant provides \(4\) set meals specifically made for choosy children, namely, Chicken Burger, Vegetable Frenzy, Spicy Gala and Steak.

Adam doesn't eat chicken and vegetable; Ben doesn't eat spicy food; Carrie doesn't eat chicken; and David doesn't eat beef. In how many ways can Mum order for a different set meal for each of the \(4\) children such that all end up satisfied? (The children don't want to be called "copycats" so they all want different set meals from each other.)

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