you are actually missing somemore possibilities here. you are taking into account only .... JSBGBGBG,BGJSBGBG,BGBGJSBG.BGBGBGJS and SJGBGBGB,GBSJGBGB,GBGBSJGB,GBGBGBSJ then what about GJSBGBGB,GBGJSBGB and so on... ?? and BGJSBGBG,BGBGJSBG..and so on ??...even in these cases...john and suzane are beside each other....SO! there are actually 7 + 7 =14 ways... Hence the answer is..2*4!*4! -2*7*3!*3! Hope this helps understand!! :-) Goodluck!!