Need help with some questions ASAP. Relatively simple perms and combs Q (1 Viewer)

[Plshelpmewithmaths]

a) Number of ways a 6 player soccer team out of a selection of 15 people.
b) Hence, what is probability of Player A being accepted into the team while Player B isn’t?

 

[Anaya R]

a) 15 C 6
b) If A is selected and B is not, we take them out of the total
so it'll be 13 C 5 I think

 

[Plshelpmewithmaths]

what about this?
a)11 people: 4 teachers, 2 parents, 5 students. Total number of arrangements in which teachers sit together but no teacher sits next to a student.
b) one of the students came with their parent. Find the probability that this student sits next to their parent.

btw this is on a round table (circle arrangement)

 

[Anaya R]

what about this?
a)11 people: 4 teachers, 2 parents, 5 students. Total number of arrangements in which teachers sit together but no teacher sits next to a student.
b) one of the students came with their parent. Find the probability that this student sits next to their parent.

btw this is on a round table (circle arrangement)

a) it'll be 5!x2!x4!x3! since the teachers have to sit next to each other (hence 4!), the students will be sitting next to each other (hence 5!) and the parents will be separating them in 2! ways. Then there are 3! ways to arrange the 4 'groups'.
b) p(student with parent) = (9!x2!)/10!
- 9! for the ways to arrange the bunch where the student and parent are grouped
- 2! for the ways to arrange the student and parent
If I am wrong please lmk. I'm a bit rusty with perms and combs

 

[Plshelpmewithmaths]

a) it'll be 5!x2!x4!x3! since the teachers have to sit next to each other (hence 4!), the students will be sitting next to each other (hence 5!) and the parents will be separating them in 2! ways. Then there are 3! ways to arrange the 4 'groups'.
b) p(student with parent) = (9!x2!)/10!
- 9! for the ways to arrange the bunch where the student and parent are grouped
- 2! for the ways to arrange the student and parent
If I am wrong please lmk. I'm a bit rusty with perms and combs

I had smth like this cuz pre sure u have to fix one of the elements?

 

[Anaya R]

View attachment 36117

I had smth like this cuz pre sure u have to fix one of the elements?

Well, since the teachers can't be next to students the inference is to be next to parents