In how many ways can 8 people, A, B, C, D, E, F, G, H be seated in a row such that C and D are not ...
In how many ways can 8 people, A, B, C, D, E, F, G, H be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
Answer/Solution
40224
Steps/Work
Number of total arrangements = 8!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
8! - (4!*2*2) = 40320 - (24*2*2) = 40224
Answer D
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
8! - (4!*2*2) = 40320 - (24*2*2) = 40224
Answer D