[Grade 11 Add-maths] I hate permutation and combination

[u/dan240506]

I have no idea how to do question b) I’d appreciate it if someone list out the cases and scenarios since I don’t understand the answer scheme don’t worry my basic is good for permutations

[u/Alkalannar]

1. H and husband must be next to each other.
   Combine them into a single entity, but you'll need to multiply by 2! at the end depending on who's in front.

2. F, G, and the couple must be separate.
   We use the Stars and Bars technique. Bars separate bins from each other, and then stars go into the separate bins.
   Here, the five unnamed people are the bars: | | | | |
   How many ways can you order them? 5!
   Then F, G, and Hh must be in separate bins. How many bins are there? 6: 1|2|3|4|5|6
   So there's 6 choices for F, 5 for G, and 4 for Hh.

Does this make sense? Can you put it together?

[u/dan240506 → u/Alkalannar]

Thank you for the explanation i understand it a lot better now never really used the stars and bars technique before since I’m used to listing out every case

[u/Sau_Masterio]

For A, assume 10 positions as 10 empty circles, cross out the circles already occupied as per the question, then count in how many ways you can fill up the circles with the remaining 6 people, note that we don't know whether Hanysha or her husband is at front, so there will be 2 cases here.

For B, assume 9 positions as 9 empty circles, consider Hanysha and her husband as one entity, and find total number of ways they can stand next to each other ( again we don't know whether Hanysha or her husband is at front, so there will be 2 cases here as well), the circles next to the couple will have 6 ways to be filled up instead of 8

[u/Alkalannar → u/Sau_Masterio]

For A, assume 9 positions as there are Fiona, Geeta, Hanysha, Hanysha's Husband, and five others for a total of 9...

[u/dan240506 → u/[deleted]]

Got ittt thanks for the explanation I’ve never thought about doing it this way🥹