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Can you tell the answer of the following questions?

1. A class of 30 students take a full row at a movie theater. There are six couples who must sit together. In how many different arrangements can the students sit?

2. A political debate has 8 pro-war attendees (PWAs) and 7 anti-war attendees (AWAs). The organizers want to seat the attendees next to each other, but with no two PWAs next to each other and no two AWAs next to each other. How many seating possibilities are there?

Can you tell the answer of the following questions?

1. A class of 30 students take a full row at a movie theater. There are six couples who must sit together. In how many different arrangements can the students sit?

2. A political debate has 8 pro-war attendees (PWAs) and 7 anti-war attendees (AWAs). The organizers want to seat the attendees next to each other, but with no two PWAs next to each other and no two AWAs next to each other. How many seating possibilities are there?

1. tie six people and treat them like a 1 person. So, there are 24 + 1 people sitting at front row.

Possible arrangement = 25!
However, in a group of six, they can switch seats within the group
Total possible arrangement = 6! x 25!

[ 1. tie six people and treat them like a 1 person. So, there are 24 + 1 people sitting at front row.

Possible arrangement = 25! However, in a group of six, they can switch seats within the group Total possible arrangement = 6! x 25!

just like to modify your answer to understand if i am getting the question right

6 couples so 12 people

30 -12+1 = 19

Possible arrangement = 19!
in a group of six, they can switch seats within the group = 6! * 25!
Again each couple can interchange thier place = 2! * 6! * 25!

I think you need to modify you solution. When they say six couples should sit together they mean 6 different couples. As in the requirement is only that each partner is paired with the other. hence 6 groups of 2

now : 18 singles, 6 couples (each couple can exchange seets)

= (18+6)! *2 should be the answer .. or am i missing some thing?

b) there is only one assignment PAPA...PAP but they can change with in a group = 8!7! (prowar!*anti!)

[quote="budugu"]I think you need to modify you solution. When they say six couples should sit together they mean 6 different couples. As in the requirement is only that each partner is paired with the other. hence 6 groups of 2

now : 18 singles, 6 couples (each couple can exchange seets)

= (18+6)! *2 should be the answer .. or am i missing some thing?

A class of 30 students take a full row at a movie theater. There are six couples who must sit together. In how many different arrangements can the students sit?

A class of 30 students take a full row at a movie theater. There are six couples who must sit together. In how many different arrangements can the students sit?

Bundle each couple as one unit. So there are 6 units

My question is why not multyple by another 6! for among couples.

24!*(2^6)*6!

You cannot because there are only 6 couples. factorial is applied as a whole not for n such couples

18 singles and 6 couples are considered as total and hence 24! ways. So the factorial you are looking for is taken care of

each couple can be arranged in 2! ways. if the question was about triplets and not couples it would be 3! ways. but still you would only multiply by 6 because there are only 6 of them

each couple can be arranged in 2! ways. if the question was about triplets and not couples it would be 3! ways. but still you would only multiply by 6 because there are only 6 of them

jainvineet and x2suresh had the right answer above. You don't want to multiply by 6, you want to multiply by 2 six times; since you have 2 choices for how to arrange each of the six couples, you have 2x2x2x2x2x2 = 64 ways to arrange the six couples in total. That of course then needs to be multiplied by 24!.
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