Question:

Thundy, Bella, and Momo are going to buy a ball each. Momo says he will not buy a football. How many ways are there for them to buy the balls? Fill in the blanks with all the possible ways.

Solution:

Let's find all the possible ways for 1 person before moving on to the next person. Thundy can buy a football, so 1 and 4 are a pair; he can buy a basketball, so 1 and 5 are a pair; and he can buy a volleyball, so 1 and 6 are a pair. Thundy has 3 possible ways. The same goes with Bella. Her pairs are: 2 and 4, 2 and 5, 2 and 6. Bella also has 3 possible ways. Finally, let's look at Momo. Remember, he will not buy a football. So his pairs are: 3 and 5, 3 and 6. That's 2 possible ways. In total, there are 3+3+2=8 possible ways for them to buy the balls.

Solution:

We can either start with route ① or route ②. Let's find all the possibilities that starts with route ① first.

①+③ can lead to Bella's house. ①+④ can lead to Bella's house. ①+⑤ will work, too! So, that's 3 ways.

How about if we start with route ②? Either ②+③, ②+④, or ②+⑤ can lead to Bella's house. So, that's 3 more ways.

In total, there are 3+3=6 ways for Momo to reach Bella's house.