Hi Alez, there is a very simple way to think about Perms and Combs.
You want to make 3 digit numbers. So you have three boxes to fill. I like to think concrete on this one because it makes it easy to see.
The three boxes are digits box, tens box and hundreds box. You have 5 different numbers you can put into these boxes.
Repeating Numbers allowed
Always start with the box with the special condition placed on it.
DIGIT BOX: You must make an even number, so only 2, 4 and 6 can go in the digits box - 3 choices only.
TENS BOX: You can use 2, 3, 4, 5 or 6 - 5 numbers to choose from.
HUNDREDS BOX: You can use 2, 3, 4, 5 or 6 - 5 numbers to choose from.
All three conditions must be met at the same time (this is an AND condition) and so we MULTIPLY all our choices.
Number of ways of making an even number with repeating digits
= 3 x 5 x 5 = 75
Repeating Numbers Not Allowed
Always start with the box with the special condition placed on it.
DIGIT BOX: You must make an even number, so only 2, 4 and 6 can go in the digits box - 3 choices only.
TENS BOX: Since you cannot repeat a number, that number is no long available. This leavs you with only 4 choices.
HUNDREDS BOX: Now you have already used 2 numbers and so only have 3 choices remaining.
All three conditions must be met at the same time (this is an AND condition) and so we MULTIPLY all our choices.
Number of ways of making an even number without repeating a digit
= 3 x 4 x 3 = 36
Hope that helps some.
