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?
I can't solve these ARrrr, please help
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?
For part (b) you must count 3-D’s and 6-R’s. How can they be arranged?
I got the answer already
6! = amount of ways of change
on a dice, let a face to be 1, then the opposite face must be another no., then the other 4 faces will change when we rotate the dice, which will result in 4 results ( 90--> 180--> 270 --> 360)
and therefore the amount of repetitions is 6 * 4 = 24
then therefore the answer is 6!/24 = 30