dddanny2006 wrote:Greg, Marcia, Peter, Jan, Bobby and Cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. If Marcia and Jan will not sit next to each other, in how many ways different arrangements can the 6 people sit?
Good arrangements = total arrangements - bad arrangements.
Total arrangements:
Number of ways to arrange the 6 elements G, M, P, J, B and C = 6! = 720.
Bad arrangements:
In a BAD arrangement, M and J are in adjacent positions.
Put M and J together in a BLOCK, so that MJ serves as SINGLE ELEMENT in the arrangement.
Number of ways to arrange the 5 elements MJ, G, P, B and C= 5! = 120.
in each of these arrangements, MJ can be reversed to JM, DOUBLING the total number of options.
Thus, we multiply by 2:
2*120 = 240.
Good arrangements:
Total-bad = 720-240 =
480.
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