Question: Delegates from 10 countries are to be seated in arow. How many differe

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Question: Delegates from 10 countries are to be seated in arow. How many different arrangements are possible if the French andEnglish delegates are to be seated next to each other, and theRussian and US delegates are not to be next to each other? Help! Don't know how to solve! Question: Delegates from 10 countries are to be seated in arow. How many different arrangements are possible if the French andEnglish delegates are to be seated next to each other, and theRussian and US delegates are not to be next to each other? Help! Don't know how to solve!

Explanation / Answer

French and English are to be together.Therefore they form one group.
French and England can be arranged in 2!Ways.
Then the total there are 9 groups now, they can be arranged in 9!Ways. Total ways of arrangement =2X9! If Russian and U.S. Also form a group,then total 8 groups can be arranged in 8! Ways. French and English; Russian andU.S. Amongst themselves   can be arranged in2! ways each Total number of such arrangements = 8!X 2! X  2! Number of required arrangements in which Frenchand English are together but Russian and U.S. are nottogether is given by = 2 X 9! -8! X 2! X2!                                   =  564480
                                  =  564480

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