Combining Combinations

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Combo-Permute Principle
To calculate permutations, you multiply by the number of possible elements each time. You can do the same thing for groups of elements. For example, if you need to choose fruit and snack for your lunch, you can just multiply the possible fruit combos by the snack combos to get the total number of possible combinations. This is because for each fruit combo, you can try any possible snack combo.

Sometimes the choices have limitations and you need to pick between two different options, such as A and B. In such a case, you need to add the A possibilities to the B possibilities to get the total number of possibilities.

You are packing a suitcase for a trip. You need to pack 7 from 10 shirts and 4 from 8 pairs of pants.
In addition, you want to take 3 fruit or melons (to eat). You have 2 melons and 4 other fruit. You can take any fruit combination except for 2 melons together.

Own Pack
Shirts 10 7
Pants 8 4
Fruit 6 3*

* No 2 melons together.


How many possible ways are there for you to pack your suitcase (according to the above rules)?

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