Grid

Example 1: Tree diagram

How many possibilities are there to throw at least 16 with three dice?

Answer:
Start with choosing the largest possibility.
You can make a tree diagram to do this systematically.

There are 10 possibilities to throw at least 16 with three dice.

Example 2: Grid/table

How many possibilities are there to throw at least 9 with two dice?

Answer:
Because we are dealing with two dice, you can use a scheme to easily show the different possibilities of throwing with two dice.
table in which the spots are added, one dice vertically and the is horizontally
There are 6 possibilities to throw at least 9 with 2 dice.

Example 3: Road diagram

Use the digits 2, 3, 4, 5 en 6 to make a 4-digit number, in which you may use the digits more than once.
How many numbers greater than 5400 can be made?

Answer:
Now we can use a 'road diagram'.
If the first digit is a 5, the second digit must be a 4, 5 or 6 and for the third and fourth digit there are no limitations.
If the first digit is a 6, there are no limitations for the second, third and fourth digit.

	3 × 5 × 5 = 75
	5 × 5 × 5 = 125

There are 75 + 125 = 200 numbers that can be made greater than 5400.

Example 4: Road diagram

Use the digits 2, 3, 4, 5 en 6 to make a 4-digit number, in which you may use the digits only once.
How many numbers greater than 5400 can be made?

Answer:
If we start with a 5, the second digit can only be a 4 or 6.
If the second digit is a 4, there are only three possibilities for the third digit (we already used two). The same applies for a 6.
In both cases you will have two possibilities left for the fourth digit.

If we start with a 6, there are four possibilities for the second digit, three possibilities for the third digit and two possibilities for the fourth digit.

	2 × 3 × 2 = 12
	4 × 3 × 2 = 24

There are 12 + 24 = 36 numbers that can be made greater than 5400.