Captaingmat wrote:2 men, 3 women and 5 chairs. How many ways if no two men sit together?
I dont know the answer. I got 8 ways.
Let A and B = the 2 men and C, D, and E = the 3 women.
Good arrangements = total arrangements - bad arrangements.
Total arrangements:
Number of ways to arrange the 5 elements A, B, C, D and E = 5! = 120.
Bad arrangements:
In a BAD arrangement, A and B are in adjacent positions.
Put A and B together in a BLOCK, so that AB serves as SINGLE ELEMENT in the arrangement.
Number of ways to arrange the 4 elements AB, C, D, and E = 4! = 24.
in each of these arrangements, AB can be reversed to BA.
Thus, we multiply by 2:
2*24 = 48.
Good arrangements:
Total-bad = 120-48 =
72.
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