Permutations and Combinations (1 Viewer)

[faisalabdul16]

Find the number of ways in which 4 girls and 3 boys can be seated in a row so that no two boys are next to each other.

Need confirmation to my answer.

 

[Squar3root]

not sure if correct tho.

= all combinations - boys sitting together
= 4!*3! - 5!/3!
= 124

must be a 4U question lol. I think in 3U the hardest it every gets is 2 boys and then you do the usual

 

[Squar3root]

ohh wait, the only possible arrangement is

G B G B G B G

= 4!*3! = 144

so answer = 144?

 

[Squar3root]

I see Drongoski on this thread so he'll confirm for you

 

[panda15]

ohh wait, the only possible arrangement is

G B G B G B G

= 4!*3! = 144

so answer = 144?

G B G B G B G
B G B G B G G
B G G B G B G
B G B G G B G
G G B G B G B

So I think it would be 5*144?

I dunno. I hated perms and combs.

 

[Squar3root]

G B G B G B G (1)
B G B G B G G (2)
B G G B G B G (3)
B G B G G B G (4)
G G B G B G B (5)

So I think it would be 5*144?

I dunno. I hated perms and combs.

ohh i didn't think of those cases (lol square missed 80% :/)

but yeah that seems "more right"

EDIT:
[soz for labeling your post]

but aren't cases 2 & 4 "the same" because they are just "shifted" likewise all the others?

 

[faisalabdul16]

ohh wait, the only possible arrangement is

G B G B G B G

= 4!*3! = 144

so answer = 144?

you can have G G B G B G B or B G G B G B G, there's more arrangements to not allow two boys to be together. It just seems ambiguous and the way i did it seems dodgy

 

[Squar3root]

was your answer 720?

 

[Squar3root]

maybe you could post your solution? lol

 

[faisalabdul16]

If 5*144 means 5x144 then i got 720 as well. but not too sure if correct.

 

[Squar3root]

If 5*144 means 5x144 then i got 720 as well. but not too sure if correct.

well if more than 2 people got it them I'm sure it is correct

 

[faisalabdul16]

What i did was total combinations so 7! - (3x6!x2)

There are three boys, and total number of ways arranging two of them together is 3x6!x2!

 

[panda15]

ohh i didn't think of those cases (lol square missed 80% :/)

but yeah that seems "more right"

EDIT:
[soz for labeling your post]

but aren't cases 2 & 4 "the same" because they are just "shifted" likewise all the others?

They're different because it's in a row. in (2) the 5th seat is a boy, in (4) it's a girl which is a different combination for the whole row.

 

[faisalabdul16]

well if more than 2 people got it them I'm sure it is correct

True true haha

 

[Squar3root]

They're different because it's in a row. in (2) the 5th seat is a boy, in (4) it's a girl which is a different combination for the whole row.

ohh yes because it is a permutations not a combination so the order is important.

soz, engrish is not my strong suite

 

[dunjaaa]

This question involves the inclusion-exclusion principle. What I typically do for these types of questions is use spaces. So sit the girls down and leave spaces in between. E.g. _G(1)_G(2)_G(3)_G(4)_. Now notice how there's 5 potential spots that the boys can sit since the question says no two boys can sit together which implies that they are separated by all the girls. Out of the 5 spots, we choose 3 boys. But bear in mind the boys can be arranged in 3! ways and the girls in 4! ways. So by the multiplication principle, the total number of arrangements is 5C3 x 3! x 4! = 1440 ways

 

[Squar3root]

This question involves the inclusion-exclusion principle. What I typically do for these types of questions is use spaces. So sit the girls down and leave spaces in between. E.g. _G(1)_G(2)_G(3)_G(4)_. Now notice how there's 5 potential spots that the boys can sit since the question says no two boys can sit together which implies that they are separated by all the girls. Out of the 5 spots, we choose 3 boys. But bear in mind the boys can be arranged in 3! ways and the girls in 4! ways. So by the multiplication principle, the total number of arrangements is 5C3 x 3! x 4! = 1440 ways

Are you just making up principles?

Notsureifsrs

 

[braintic]

I'm getting 1440

 

[dunjaaa]

Nope

 

[braintic]

This question involves the inclusion-exclusion principle. What I typically do for these types of questions is use spaces. So sit the girls down and leave spaces in between. E.g. _G(1)_G(2)_G(3)_G(4)_. Now notice how there's 5 potential spots that the boys can sit since the question says no two boys can sit together which implies that they are separated by all the girls. Out of the 5 spots, we choose 3 boys. But bear in mind the boys can be arranged in 3! ways and the girls in 4! ways. So by the multiplication principle, the total number of arrangements is 5C3 x 3! x 4! = 1440 ways

Correct working, but this is not really the inclusion-exclusion principle (although that is a way of answering this question).
Inclusion-exclusion involves subtracting/adding intersections of sets, based on a Venn diagram.