Question

Afirm works 7 days a week. Every employee must work exactly 3 full days and 4 half-days each week. A half-day can be either morning or afternoon, and two half-days cannot be held on the same day. a) How many possible different weekly schedules are there? 560 Expected answer: 560

Answer 1

a) 560 (as you know)

Explanation:

There are 7C3 = 35 ways to choose 3 full-time days from 7.

There are 2^4 = 16 ways to choose a half-day each day from the remaining 4 days.

The total number of possible schedules is ...

35×16 = 560

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nCk = n!/(k!(n-k)!)

7C3 = 7·6·5/(3·2·1) = 7·5 = 35