In how many Different Ways? Combination Problems

Let's solve the following problem:

Step 1

We find the number of possible ways to arrange the three cubes by first putting the red cube first.

There are two ways here:

• red, blue, green
• red, green, blue

Step 2

We find the number of possible ways to arrange it, this time putting the blue cube first.

Here again there are two ways:

• blue, red, green
• blue, green, red

Step 3

Lastly we put the green cube in first place.

Here again there are two ways:

• green, blue, red
• green, red, blue

Answer: 2 + 2 + 2 = 6 ways

* Combinatorics problems can be found in the course Competitive Mathematics - Level 2