After a long day of work, Gertrude stops by the bakery to purchase some cookies

After a long day of work, Gertrude stops by the bakery to purchase some cookies.

Because the bakery is about to close, there is not much to choose from. There are:

? 7 oatmeal raisin cookies

? 1 chocolate chip cookie

? 2 ginger snaps

? 1 frosted sugar cookie

? 1 shortbread cookie

? 2 peanut butter cookies

? 2 snickerdoodles

Gertrude wishes to take 4 cookies home with her. Gertrude refuses to eat oatmeal raisin cookies, so she

won't purchase them. Excluding oatmeal raisin, she calculates that she can purchase 48 distinct groups of

cookies using the following math (note that she is willing to buy more than one of the same cookie):

6C4 + 3C1 × 5C2 + 3C2 = 48

Provide a written justification for how Gertrude counted her number of possible cookie groups.

In this justification, discuss: what the three individual terms ( 6C4, 3C1 × 5C2, and 3C2) each represent with relation to this

problem (including what n and k in each nCk refer to). why there is addition or multiplication between the C-formulas.