# Permutation and Combination problem

• April 27th 2008, 04:23 AM
hkdrmark
Permutation and Combination problem
The diagram shows a gird measuring 4 cm by 6 cm. The aim is to get from point A in the top left - hand corner to point B in the bottom right-hand corner by moving along the black lines either downwards or to the right. A single move is defined as shifting along one side of a single square, thus it takes you ten moves to get from A to B.

sorry I haven't got the diagram here....

a) How many different routes are possible?

b) How many different routes are possible if you cannot move along the top line of the grid?

c) How many different routes are possible if you cannot move along the second row from the top of the grid?

2) a) the six faces of a number of identical cubes are painted in six distinct colours. How many different cubes can be formed?

b) A die fits perfectly into a cubical box. How many ways are there of putting the die into the box?

• April 27th 2008, 04:27 AM
Isomorphism
Quote:

Originally Posted by hkdrmark
The diagram shows a gird measuring 4 cm by 6 cm. The aim is to get from point A in the top left - hand corner to point B in the bottom right-hand corner by moving along the black lines either downwards or to the right. A single move is defined as shifting along one side of a single square, thus it takes you ten moves to get from A to B.

sorry I haven't got the diagram here....

a) How many different routes are possible?

b) How many different routes are possible if you cannot move along the top line of the grid?

c) How many different routes are possible if you cannot move along the second row from the top of the grid?

Sorry i cant understand what you are saying :(

Quote:

Originally Posted by hkdrmark
2) a) the six faces of a number of identical cubes are painted in six distinct colours. How many different cubes can be formed?

$6^6$:Because each of the faces can be painted in 6 different ways and there are 6 faces :)

Quote:

Originally Posted by hkdrmark
b) A die fits perfectly into a cubical box. How many ways are there of putting the die into the box?

What has a die got to do with coloured cubes? (Wondering)
• April 27th 2008, 05:02 PM
hkdrmark
Arrgghh can anyone help me ?

These questions are from my text book, sorry I can't explain the question because I can't solve it!(Headbang)(Headbang)
• April 27th 2008, 05:08 PM
hkdrmark
Quote:

Originally Posted by Isomorphism
Sorry i cant understand what you are saying :(

$6^6$:Because each of the faces can be painted in 6 different ways and there are 6 faces :)

What has a die got to do with coloured cubes? (Wondering)

it is 30
• April 27th 2008, 05:16 PM
Plato
Quote:

Originally Posted by hkdrmark
The diagram shows a gird measuring 4 cm by 6 cm. The aim is to get from point A in the top left - hand corner to point B in the bottom right-hand corner by moving along the black lines either downwards or to the right. A single move is defined as shifting along one side of a single square, thus it takes you ten moves to get from A to B.

a) How many different routes are possible?
b) How many different routes are possible if you cannot move along the top line of the grid?
c) How many different routes are possible if you cannot move along the second row from the top of the grid?
For part (a) you must count 4-D’s and 6-R’s. How can they be arranged?
$\frac {10!}{(4!)(6!)}?$

For part (b) you must count 3-D’s and 6-R’s. How can they be arranged?
• April 27th 2008, 05:19 PM
hkdrmark
Quote:

Originally Posted by Plato
a) How many different routes are possible?
b) How many different routes are possible if you cannot move along the top line of the grid?
c) How many different routes are possible if you cannot move along the second row from the top of the grid?
For part (a) you must count 4-D’s and 6-R’s. How can they be arranged?
$\frac {10!}{(4!)(6!)}?$

For part (b) you must count 3-D’s and 6-R’s. How can they be arranged?

you are great! thanks!
• April 27th 2008, 07:19 PM
Isomorphism
Quote:

Originally Posted by hkdrmark
it is 30

Ya sorry...
But I dont think it is 30 either...

There are 6 faces. Each face can be colored in 6 different colors...
I can either choose all colors same in 6 ways.
I can either choose all colors except 1 same in 6 x 5C1 = 30 ways.
It is already greater than 30 :(
• April 27th 2008, 07:29 PM
hkdrmark
Quote:

Originally Posted by Isomorphism
Ya sorry...
But I dont think it is 30 either...

There are 6 faces. Each face can be colored in 6 different colors...
I can either choose all colors same in 6 ways.
I can either choose all colors except 1 same in 6 x 5C1 = 30 ways.
It is already greater than 30 :(