Delegates from 10 countries, including Russia,

France, England, and the United States, are to

be seated in a row. How many different seating arrangements are possible if the French and

English delegates are to be seated next to each

other and the Russian and U. S. delegates are not

to be next to each other

Answer: 564480 arrangements

Step-by-step explanation:

First, let's consider the French and English delegates as one party because they will sit next to each other.

So total delegates if French and English are always together comes out to be 9 instead of 10.

Now, they are to sit in a row and can have different seats so the total number of ways they can sit is = 2 x 9! = 725760 ways.

Now, when Russian and U. S delegates are not to sit next to each other so consider similarly like before consider them as one unit like French and English. Now they can also change their seats so number of way for them = 2 x 2 x 8! = 161280 ways

To find out when French and English delegates are together and Russain and U. S delegates are not together we subtract the way from the original value.

725760-161280 = 564480 way.

564,480

Step-by-step explanation:

The appliocation of factorial n! = n (n-1) (n-2) (n-3) ...

Arrangement when french and English delegates are to seat together;

since we have 10 delegates, Freench and english will be treated as 1 delegates as such we have 9groups. The number of ways of arranging 9groups = 9! and if the french and English are to be treated as a group = 2!

Hence, number of ways of arrangement = 9! x 2! = 725,760

In this case, English and french are to be seated next to each other while russia and US delegates are not to seat nect to each other; both groups will be treated as 2 as such we have 8groups, the number of ways of arranging 8groups = 8!

french and english together = 2!

Russia and US together = 2!

The number of ways of arrangement = 8! x 2! x 2! = 161,280

hence the number of ways of arranging 10 delegates if french and english are to be seated next to each other and Russia and US are not to be seated next to each other;

N = 725,760 - 161,280 = 564,480