five children, Arya, Betsy, Chen, Daniel, Emily, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?  Choose one
A) 240  B) 480  C) 540  D) 72  E) 840
Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..   total ways = 5!..   ways B and E will be sitting together..   take both B and E as one, then these two together with other 3 can sit in 4! ways ...   Also B and E can sit within themselves in 2! ways..   so the answer required = 5!-2*4!=72..   72
<result>D</result>
five children, Arya, Betsy, Chen, Daniel, Emily, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?