# Perms and combs help please! (1 Viewer)

#### flowerp

##### Active Member
Hi every1 I need help with the following questions please:

In how many ways can 5 boys and 4 girls be arranged in a line if:

A) three boys must start the line
B) a particular boy, John, insists on being between 2 girls

Thanks

#### HeroWise

##### Active Member
So part A ) I would Arrange those 3 boys by 5!/2! and arrange the rest in 6! ways so 5P3.6!=43200

And B) He is legit sandwiched, so Alyssa and janet can arrange themselves in 2 ways so 2! and he is there so only one way the rest can arrabe in 6! but Alyssa and jannet can move around with John cena 7 times hence 2!7! total ways

#### integral95

##### Well-Known Member
Hi every1 I need help with the following questions please:

In how many ways can 5 boys and 4 girls be arranged in a line if:

A) three boys must start the line
B) a particular boy, John, insists on being between 2 girls

Thanks
a)
For the first 3 spots you have to select 3 boys from 5 and understand that the order amongst those 3 matters so it's 5P3, then for the remaining 6 people it's just 6!

(5P3)*6!

b)

First you select 2 girls from 4, so that's 4C2, you form that with John to make one group, also multiply that by 2 as the girls could be interchanged
(e.g a group of A John B is different to B John A) so now you have 7 "groups " to rearrange so it's 7!

(4C2)*2*7!

Not 100% sure with b) tbh.

#### integral95

##### Well-Known Member
So part A ) I would Arrange those 3 boys by 5!/2! and arrange the rest in 6! ways so 5P3.6!=43200

And B) He is legit sandwiched, so Alyssa and janet can arrange themselves in 2 ways so 2! and he is there so only one way the rest can arrabe in 6! but Alyssa and jannet can move around with John cena 7 times hence 2!7! total ways
You didn't account for the other 2 possible girls.

#### HeroWise

##### Active Member
You didn't account for the other 2 possible girls.

Pfft I read it wrong lol

Anyway, if these girls are not particular, it becomes 4*3*6!*7 = 12*7! which is the same as integral95's answer

pppffffftttt i thought beween two particular girls. boring quesiton

#### micsthepick

##### New Member
really the question should be specific in it's wording and say "between any two girls"

#### HeroWise

##### Active Member
Lol, this John guy is a player

Well jokes aside b yeah its a bit ambiguous

#### flowerp

##### Active Member
Thank you sooo much everyone !!!!

#### flowerp

##### Active Member
a)
For the first 3 spots you have to select 3 boys from 5 and understand that the order amongst those 3 matters so it's 5P3, then for the remaining 6 people it's just 6!

(5P3)*6!

b)

First you select 2 girls from 4, so that's 4C2, you form that with John to make one group, also multiply that by 2 as the girls could be interchanged
(e.g a group of A John B is different to B John A) so now you have 7 "groups " to rearrange so it's 7!

(4C2)*2*7!

Not 100% sure with b) tbh.
Hey, why do we do 4C2 and not 4P2?? Thx

#### HeroWise

##### Active Member
Which girl u pick doesnt matter, ORder is not important if that helps