combinatorics

[kikar]

:zzz: :zzz: :zzz:

[vsage]

2. Reduce the problem to a simpler one and find a pattern. For example, in a 2x2 square only 4 triangles have this property.
3. Could you give the exact wording of the question or rephrase it? I am unsure if you mean one quarter of all subsets of integers 1,2,3...m with three elements or not.

[TenaliRaman]

1> How many arrangements are there such that no two A's are beside each other?
2> shouldn't be a problem .... straightforward (only thing to remember ... 3 points cannot be collinear)
3> how many 3-subsets can you form? (call this A)
How many 3-subsets can contain integer 5? (call this B)
1/4 * A = B ... solve for m
4> no three segments cross at any point ....
therefore atmost two segments can cross each other ...
and every crossing of two segments produces 1 intersection point ...
so ??

-- AI

[kikar]

Could you give the exact wording of the question or rephrase it? I am unsure if you mean one quarter of all subsets of integers 1,2,3...m with three elements or not.

a subset with 3 elements

TR.. im so lost

could u explain it a lil more?

and number one i know its ez but I cant seem to get it

[TenaliRaman]

1> How many arrangements are there such that no two A's are beside each other?

a .. First arrange the B's and y's? in how many ways can u do this?
b .. amongst 6 B's and 7 y's there are 14 places where i can place A (why do i do this ? u see this way no two A will be beside each other)
c .. in how many ways can i arrange the A's in these 14 places

Can u proceed from here .... ??

shouldn't be a problem .... straightforward (only thing to remember ... 3 points cannot be collinear)

Look at what i gave in the brackets ... can u see how to pick the points then?

how many 3-subsets can you form? (call this A)
How many 3-subsets can contain integer 5? (call this B)
1/4 * A = B ... solve for m

Can u find A and B? (atleast A is pretty simple)

4> no three segments cross at any point ....
therefore atmost two segments can cross each other ...
and every crossing of two segments produces 1 intersection point ...
so ??

How many segments are given?
In how many ways can i choose 2 segments out of the given number of segments?

-- AI

[kikar]

TR.. ur help is greatly appreciated

A .. First arrange the B's and y's? in how many ways can u do this?
you can arrange this in 13! ways because thats how many total letters there are?

i LOST you from here :(

Look at what i gave in the brackets ... can u see how to pick the points then?


This i dont get at all


Can u find A and B? (atleast A is pretty simple)
got this thanks

and the last one i dont get at all too

man... i raped the test on this unit, but the teahers chellenge sets are HARD

[kikar]

Anyone??????

[kikar]

can the mods delte this thread pleez