Answer:
chocolate chip cookie first: 15 ways
chocolate chip cookie last: 15 ways
chocolate chip cookie first and last: 5 ways
Step-by-step explanation:
There is a total of 7 cookies.
Is she eats a chocolate cookie first, she will have 2 chocolate cookies and 4 sugar cookies (6 in total).
So, to find the number of different orders that Amy can eat the remaining cookies, we just need to calculate a combination of 6 choose 2 (that is, the number of ways we can put the 2 chocolate cookies among the 6 cookies) or a combination of 6 choose 4 (same thing, but for the sugar cookies):
C(6,2) = 6! / (2! * 4!) = 6 * 5 / 2 = 15 ways
Is she eats a chocolate cookie last, she will have 2 chocolate cookies and 4 sugar cookies (6 in total), so the problem is solved again with a combination of 6 choose 2:
C(6,2) = 15 ways
Is she eats a chocolate cookie first and last, she will have just 1 chocolate cookie left and 4 sugar cookies (5 in total), so the problem is solved with a combination of 5 choose 1 or a combination of 5 choose 4:
C(5,1) = 5! / (1! * 4!) = 5 ways
