Subject: Functions
Name: Rachel
Who is asking: Student
Level: Secondary

I need help with these two problems! The teacher didn't explain clearly on how to do it. I'm lost! Please help. Thanks

How many different numbers of 2 different digits each can be formed using the digits (1,3,5,7,9)?

How many triangles are formed by the vertical of a regular hexagon?

Imagine that you are goint to list all such 2 digit numbers and, at each stage, count the number of choices you have. To write a 2 digit number you start with the first digit. For this digit you have 5 choices, either 1, 3, 5, 7 or 9. Thus you list so far is

Choose one of the items on you list, say the one that starts with 7. If you want to extend this to a 2 digit number you have 4 choices for the second digit, 1, 3, 5 or 9. Thus the possible 2 digit numbers that start with 7 are

What is important to see here is that whichever 1 digit number you chose from the first list, it expands to 4, 2 digit numbers. Thus it total you have