The giftwrap desk at a store offers 5 box sizes 7 wrapping p

The gift-wrap desk at a store offers 5 box sizes, 7 wrapping papers, 4 ribbon colors, 3 ribbon sizes, and 6 special items to be added to the box. How many ways can you gift-wrap a present if you must choose a box size and wrapping paper, but do not need to choose the other options?

Solution

There are 5*7*4*3*6 = 2520 ways if you have to choose all options.

Now, there are 5*7 = 35 options if you strictly not choose any of the last three options.

If you choose a ribbon, then there are 5*7*4*3 = 420 ways.

If you don\'t choose a ribbon but choose a special item, there are 5*7*6 = 210 ways.

Thus, there are a total of 2520 + 35 + 420 + 210 = 3185 WAYS. [ANSWER]