# How many ways are there to choose 16 cookies?

How many ways are there to choose 16 cookies if there are six varieties of cookies including chocolate chip, and at least six chocolate chip cookies must be chosen?

Is $C(n+r-1,n-1)$ correct where $n=16$ and $r=6$?

(There is an unlimited amount of each typy of cookie)

• Are you assuming unlimited quantity of each type of cookie? – jdods Aug 5 '15 at 15:08
• @jdods Yes there is – Julia Aug 5 '15 at 15:10
• Do you mean permutations (specific orderings) or combinations ? – David Quinn Aug 5 '15 at 15:10
• @DavidQuinn Combinations – Julia Aug 5 '15 at 15:10
• So now the question reduces to choosing $10$ cookies out of $6$ varieties, with no restrictions. Can you handle this ? – Shailesh Aug 5 '15 at 15:11

$Hint:$
First take out the $6$ chocolate chip cookies anyways. Now the problem reduces to choosing $10$ cookies from $6$ varieties with no restriction, which is the stars and bars problem, with $n=10$ and $r = 6$
• So is $C(n+r-1,n-1)$ correct with $n=10$ and $r=6$. I made a mistake, I meant to ask it this way, but I do not want to change the question now. – Julia Aug 5 '15 at 15:22
• The second parameter should be $r - 1$. Otherwise it sees OK. That was probably just an oversight. – Shailesh Aug 5 '15 at 15:23