Hello, I am in 6th grade and I am having some trouble with my math homework. Right now, we are learning about sample spaces. The problems I'm having trouble on are:

1) There are 5 ways to go from Town X to Town Y. There are 3 ways to go from Town Y to Town Z. How many different wys are there to go from Town X to Town Z, passing through Town Y?

and

2) Rasheed has tan pants, black pants, gray pants, and blue pants. He has a brown sweater and a white sweater. How many different ways can he wear a sweater and pants together?

Your help will be greatly appreciated!!!

Thank you, NoName (my nickname)

### 2 Answers | Add Yours

`1)` For every way you use to go from X to Y you can use one of the way to go from Y to Z so for 5 ways `X---> Y` can choice 3 ways

`Y-------->Z` for a total of `3xx5= 15 ways`

`2)` The reasonement is the same of 1).

Indeed for every pant you can use one sweater, since the pants are 3 andthe sweater 2 , then can use togeter `3xx2=6` couple

We will apply Fundamental Counting Principles here. When there are m ways to do one thing, and n ways to do another, then there are m×n ways of doing both.

So, for the number of different ways from X to Z we will have:

5*3 = **15 ways**

Same principle applies for number 2.

There are 3 different pants, and 2 different sweaters.

So, we will have 3 * 2 =** 6 ways to wear sweaters and pants together.**

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