stuck qs help needed (2 Viewers)

[kkk579]

How many rectangles can be formed from a 9 by 9 grid (including all squares)?
18b and c
q 15
q18

 

[kkk579]

Bump help pls

 

[kkk579]

bump

 

[cossine]

bump

No need to bump every 30 minutes. Have you tried math stack exchange to see if there was any similar questions.

 

[cossine]

How many rectangles can be formed from a 9 by 9 grid (including all squares)?
18b and c
View attachment 43439View attachment 43440q 15
View attachment 43441q18

Maybe you could just select a shirt then apply rule of product axiom. (Q15)

Similarly you could do same for Q18. Just place one of boys in the circle and then apply rule of product axiom

 

[kkk579]

Maybe you could just select a shirt then apply rule of product axiom. (Q15)

Similarly you could do same for Q18. Just place one of boys in the circle and then apply rule of product axiom

Whats rule of product axiom?

 

[kendricklamarlover101]

How many rectangles can be formed from a 9 by 9 grid (including all squares)?
18b and c
View attachment 43439View attachment 43440q 15
View attachment 43441q18

1) a rectangle is composed of 2 sides. in a 9x9 grid u can make a rectangle by drawing 2 lines vertically and 2 lines horizontally. theres 10 horizontal lines and 10 vertical lines and hence the number of rectangles is 10C2 x 10C2
2) https://boredofstudies.org/threads/probability-question.84117/
3) just use the complement: clothes not together = total - clothes together
4) fixing 1 girl in place and letting her sit next to a boy, girl Y can sit in 2 places and u can arrange the other girls 2! ways. similarily boy X can sit in 2 places and the other boys can sit in 3! ways. then u multiply by 2 for when the boys are on the other side of the girl u fixed in place.

its been a while since i did combinatorics tho so idk this is right lol

 

[cossine]

Whats rule of product axiom?

Basically everything in combinatorics is based on two things.

1) rule of product
2) rule of sum

An axiom is statement that is true but cannot be proven.

Rule of Product
Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions

Rule of Sum
Stated simply, it is the intuitive idea that if we have A number of ways of doing something and B number of ways of doing another thing and we can not do both at the same time, then there are A + B ways to choose one of the actions

https://en.wikipedia.org/wiki/Rule_of_product
https://en.wikipedia.org/wiki/Addition_principle

 

[kendricklamarlover101]

Basically everything in combinatorics is based on two things.

1) rule of product
2) rule of sum

An axiom is statement that is true but cannot be proven.

Rule of Product
Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions

Rule of Sum
Stated simply, it is the intuitive idea that if we have A number of ways of doing something and B number of ways of doing another thing and we can not do both at the same time, then there are A + B ways to choose one of the actions

https://en.wikipedia.org/wiki/Rule_of_product
https://en.wikipedia.org/wiki/Addition_principle

are these really axioms though? from what i remember from ext 1 is that enumerative combinatorics its built upon the addition principle, multiplication principle and the inclusion-exclusion principle, which can be all be proven.

Prove sum/product rule

How do I prove the sum/product rule in combinatorics? I think I should use induction but how do I start? What should be the base case and the ... erm induction step? Sum rule: suppose that an

math.stackexchange.com

 

[cossine]

are these really axioms though? from what i remember from ext 1 is that enumerative combinatorics its built upon the addition principle, multiplication principle and the inclusion-exclusion principle, which can be all be proven.

Prove sum/product rule

How do I prove the sum/product rule in combinatorics? I think I should use induction but how do I start? What should be the base case and the ... erm induction step? Sum rule: suppose that an

math.stackexchange.com

I will take back what I said.

 

[kkk579]

1) a rectangle is composed of 2 sides. in a 9x9 grid u can make a rectangle by drawing 2 lines vertically and 2 lines horizontally. theres 10 horizontal lines and 10 vertical lines and hence the number of rectangles is 10C2 x 10C2
2) https://boredofstudies.org/threads/probability-question.84117/
3) just use the complement: clothes not together = total - clothes together
4) fixing 1 girl in place and letting her sit next to a boy, girl Y can sit in 2 places and u can arrange the other girls 2! ways. similarily boy X can sit in 2 places and the other boys can sit in 3! ways. then u multiply by 2 for when the boys are on the other side of the girl u fixed in place.

its been a while since i did combinatorics tho so idk this is right lol

i think the ans for first one was 9c2 times 9c2
also i dont quire understand your sol for the last q and the sol in the older thread abt part c

 

[kkk579]

bump