Question

A bakery sells three kinds of rolls. How many different combinations of rolls could Jack purchase if he buys a total of six rolls and includes at least one of each kind?

Answer 1

Let's call the rolls roll A, B, and C
We can just multiply all combinations by 3 and get the answer because AAAABC would just be BBBBAC and CCCCBA following the same pattern
ABCABC

AAAABC * 3 = 3


AAABCC * 3 = 9
AAABBC


AABBCC *3 = 18
AABCCC
AABBBC

ABBBCC * 3 = 30
ABBCCC
ABCCCC
ACBBBB

Curiously enough to went 3 + 6 + 9 + 12. Answer is 30

Answer 2

10 different combinations.