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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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 seated is …​

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Alexandra 2 weeks 2021-09-10T15:37:01+00:00 1 Answer 0 views 0

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    2021-09-10T15:38:34+00:00

    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!

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18:9+8+9*3-7:3-1*13 = ? ( )