Question

8. Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives?

Answer 1

From the given information, Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated with no restrictions: That is, When there is no restriction, then the number of arrangements of 8 people (4 married couples) is, 8!-8x7x6x5x4x3x2x1 40,320 different ways In how many different ways can they be seated if each couple is to site together: Each couple is to site together, then 4-different couple can be arranged in, 4-4x3x2x1 -24 ways For each such arrangement, each member of couple can change their seat in 2!-2 ways.

So, Total number of arrangements-24x(2) 384 different ways In how many different ways can they be seated if all the husbands sit together to the right of all the wives: All the husbands sit together to the right of all the wives then the husbands can arrange in, 4! 4x3x2x1 -24 ways And the wives can have arranged in, 4! 4x3x2x1 -24 ways Therefore, the required answer is, 4!x4!- 24x24 -576 different ways