seven children, Arya, Betsy, Chen, Daniel, Emily, and Franco, 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 the most appropriate option:
A) 240
B) 480
C) 540
D) 720
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 = 6!..   ways B and E will be sitting together..   take both B and E as one, then these two together with other 4 can sit in 5! ways ...   Also B and E can sit within themselves in 2! ways..   so the answer required = 6!-2*5!=540..   ans 540
<result>C</result>
seven children, Arya, Betsy, Chen, Daniel, Emily, and Franco, 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?