Stephanie needs to work 28 hour a week, but can only work 5 days a week. She can work 5 6 7 or 8 hour days. How many combinations of four add up to 28?

Question

Stephanie needs to work 28 hour a week, but can only work 4 days a week. She can work 5, 6, 7 or 8 hour days. How many combinations of four adds up to 28?

Answer 1

5+6+7+8=26 hours, so we are 2 hours short. The following combinations add up to 28:

(5,7,8,8), (6,6,8,8), (7,7,7,7), (6,7,7,8) and their permutations: (5,7,8,8)=(7,8,8,5) for example.

Including permutations, we have:

(5,7,8,8), (5,8,7,8), (5,8,8,7), (6,6,8,8), (6,7,7,8), (6,7,8,7), (6,8,6,8), (6,8,7,7), (6,8,8,6), (7,5,8,8),

(7,6,7,8), (7,6,8,7), (7,7,6,8), (7,7,7,7), (7,7,8,6), (7,8,5,8), (7,8,6,7), (7,8,7,6), (7,8,8,5), (8,5,7,8),

(8,5,8,7), (8,6,6,8), (8,6,7,7), (8,6,8,6), (8,7,5,8), (8,7,6,7), (8,7,7,6), (8,7,8,5), (8,8,5,7), (8,8,6,6),

(8,8,7,5). The ones in bold print are in numerical order of hours.