To cheer up your friend who is safely social distancing at home, you decide to put together and send them a box of chocolates! Let j,k,l,m be natural numbers such that 1 < = k <= j and 1 <= 2l < =m. You have a total of j dark chocolates and m milk chocolates for you to choose from. All of the chocolates (even the same type) have different fillings and are therefore all distinguishable. However, you remember that l of the milk chocolates have nuts inside of them and that your friend isn't the biggest fan of nuts with milk chocolate. Thus, you decide to include one of these l milk chocolates with nuts (yes, you can include none).
Required:
How many different chocolate boxes can you form consisting of exactly k dark chocolates and l milk chocolates?