## A man invites 14 persons to a dinner and sit 8 of them at one round table and 6 at another, then the number of ways in which they can be sea

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Step-by-step explanation:MATHS

A gentleman invites 13 guests to a dinner and places 8 of them at one table and remaining 5 at the other, the tables being round. The number of ways he can arrange the guests is

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ANSWER

The number of ways in which 13 guest may be divided into groups of 8 and 5=

13

C

5

=

5!8!

13!

.

Now, corresponding to one such group, the 8 guests may be seated at one round table in (8−1)!⇒7! ways

and the five guests at the other table in (5−1)!=4! ways.

But each way of arranging the first group of 8 persons can be associated with each way of arranging the second group of 5,

Therefore, the two processes can be performed together in 7!×4! ways.

Hence required number of arrangements

=

5!8!

13!

×7!×4!=

5.4!×8.7!

13!

×7!×4!=

40

13!