Question 1046393: A parade is to include five carriages A, B, C, D and E. In how many ways can the carriages be ordered if B must not precede D?
Answer by t0hierry(194)   (Show Source):
You can put this solution on YOUR website! 3! counts how many ways you can order A,C,E. 4! will count how many ways you can order A C E D.
ACE D
AEC D
CEA D
CAE D
EAC D
ECA D
AC D E
AE D C
CE D A
CA D E
EA D C
EC D A
Repeat with D in second position, and in first.
For D in 4th position, B is imposed. So we have 6 ways.
For D in 3rd position, we have 2 possibilities for each B (2*6)
For D in 2nd position, we have 3*6 possibilities
For D in 1st position we have 4*6
Total: 6 + 2*6 + 3*6 + 4*6 + 5*6 = 15 * 6 = 90
Combinatorics is not my specialty. You might want to check I did it right.
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