# Clever counting » Diagram/Grid

## Example 1: Tree diagram

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

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?

Because we are dealing with two dice, you can use a scheme to easily show the different possibilities of throwing with two dice. There are 6 possibilities to throw at least 9 with 2 dice.

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?

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.

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? 2 × 3 × 2 = 12 4 × 3 × 2 = 24