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10-couples-are-invited-to-a-dinner-and-should-be-seated-at-a-round-table-in-how-many-ways-can-the-host-do-this-1-generally-2-if-two-men-should-not-sit-next-to-each-other-3-as-2-but-two-spe




Question Number 218299 by mr W last updated on 05/Apr/25
10 couples are invited to a dinner and  should be seated at a round table.  in how many ways can the host do  this,  1) generally  2) if two men should not sit next       to each other  3) as 2), but two speicial couples        should not sit next to each other
10couplesareinvitedtoadinnerandshouldbeseatedataroundtable.inhowmanywayscanthehostdothis,1)generally2)iftwomenshouldnotsitnexttoeachother3)as2),buttwospeicialcouplesshouldnotsitnexttoeachother
Commented by Tawa11 last updated on 05/Apr/25
I just try sir.  (1)  (20 − 1)!  = 19!  (2)   9! × 10!  (3)   9! × 10! − 2 × 8! × 10!
Ijusttrysir.(1)(201)!=19!(2)9!×10!(3)9!×10!2×8!×10!
Commented by mr W last updated on 05/Apr/25
please explain your solution for (3).    say H_i  are the husbands and W_i  are  the wives. (i=1,2,...,10)  H_1  and W_1  are the couple 1,   H_2  and W_2  are the couple 2. It is  meant that H_1  may not sit next to  W_2  and H_2  may not sit next to W_1 .  but certainly H_1  may sit next to W_1   and H_2  may sit next to W_2 .
pleaseexplainyoursolutionfor(3).sayHiarethehusbandsandWiarethewives.(i=1,2,,10)H1andW1arethecouple1,H2andW2arethecouple2.ItismeantthatH1maynotsitnexttoW2andH2maynotsitnexttoW1.butcertainlyH1maysitnexttoW1andH2maysitnexttoW2.
Commented by mehdee7396 last updated on 05/Apr/25
  9!×8!
9!×8!

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